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Physics Reports
Volumn 385, Issue 3-6, 2003, Pages 69-228
Quantum field theory in the large N limit: A review
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EID: 0141708099     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(03)00263-1     Document Type: Review
Times cited : (583)
References (242)
  • 1
    • 0141675910 scopus 로고    scopus 로고
    • Some sections are directly inspired from lectures given at 11th Taiwan Spring School, Taipei hep-th/9810198
    • Some sections are directly inspired from Zinn-Justin, J. lectures given at 11th Taiwan Spring School, Taipei, 1997; hep-th/9810198.
    • (1997)
    • Zinn-Justin, J.1
  • 2
    • 0003440273 scopus 로고
    • For a general background with analogous notation see Clarendon Press, Oxford (4th Edition 2002)
    • For a general background with analogous notation see Zinn-Justin, J. Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford, 1989 (4th Edition 2002).
    • (1989) Quantum Field Theory and Critical Phenomena
    • Zinn-Justin, J.1
  • 3
    • 36049054483 scopus 로고
    • As shown by the large N-limit of the classical N-vector model coincides with the spherical model solved in Ref. [4]
    • As shown by Stanley, H.E. Phys. Rev. 176 (1968) 718, the large N-limit of the classical N-vector model coincides with the spherical model solved in Ref. [4]
    • (1968) Phys. Rev. , vol.176 , pp. 718
    • Stanley, H.E.1
  • 5
    • 33645916042 scopus 로고
    • The modernformulationof the RG ideas is due to
    • The modernformulationof the RG ideas is due to: K.G. Wilson, Phys. Rev. B 4 (1971) 3174
    • (1971) Phys. Rev. B , vol.4 , pp. 3174
    • Wilson, K.G.1
  • 8
    • 25744447154 scopus 로고
    • The idea of the E-expansion is due to
    • The idea of the E-expansion is due to Wilson, K.G. Fisher, M.E. Phys. Rev. Lett. 28 (1972) 240.
    • (1972) Phys. Rev. Lett. , vol.28 , pp. 240
    • Wilson, K.G.1    Fisher, M.E.2
  • 9
    • 0039759450 scopus 로고
    • 113, 1074 and Refs. [9-12]
    • Abe, R. Prog. Theor. Phys. 49 (1973) 113, 1074, 1877, and Refs. [9-12]
    • (1973) Prog. Theor. Phys. , vol.49 , pp. 1877
    • Abe, R.1
  • 16
    • 4243351996 scopus 로고
    • Refs. [14,15] The spin-spin correlation in zero field is obtained in
    • The spin-spin correlation in zero field is obtained in Fisher, M.E. Aharony, A. Phys. Rev. Lett. 31 (1973) 1238 and Refs. [14,15]
    • (1973) Phys. Rev. Lett. , vol.31 , pp. 1238
    • Fisher, M.E.1    Aharony, A.2
  • 19
    • 0001450707 scopus 로고
    • The contribution of order 1/N to the equation of state is given in
    • The contribution of order 1/N to the equation of state is given in Brézin, E. Wallace, D.J. Phys. Rev. B 7 (1973) 1967.
    • (1973) Phys. Rev. B , vol.7 , pp. 1967
    • Brézin, E.1    Wallace, D.J.2
  • 20
    • 0000493586 scopus 로고
    • The exponent ω has been calculated to order 1/N by
    • The exponent ω has been calculated to order 1/N by Ma, S.K. Phys. Rev. A 10 (1974) 1818.
    • (1974) Phys. Rev. A , vol.10 , pp. 1818
    • Ma, S.K.1
  • 21
    • 85104369179 scopus 로고
    • See also the review of C. Domb, M.S. Green (Eds.), Academic Press, London
    • See also the review of Ma, S.K. in: C. Domb, M.S. Green (Eds.), Phase Transitions and Critical Phenomena, Vol. 6, Academic Press, London, 1976.
    • (1976) Phase Transitions and Critical Phenomena , vol.6
    • Ma, S.K.1
  • 22
    • 85104369179 scopus 로고
    • The study of the large N limit by the steepest descent method is explained in contribution to C. Domb, M.S. Green (Eds.), Academic Press, London It is applied to more general scalar field theories in [20]
    • The study of the large N limit by the steepest descent method is explained in Brézin, E. Le Guillou, J.C. Zinn-Justin, J. contribution to Phase Transitions and Critical Phenomena, Vol. 6, C. Domb, M.S. Green (Eds.), Academic Press, London, 1976. It is applied to more general scalar field theories in [20]
    • (1976) Phase Transitions and Critical Phenomena , vol.6
    • Brézin, E.1    Le Guillou, J.C.2    Zinn-Justin, J.3
  • 24
    • 0000757779 scopus 로고
    • For a Hartree-Fock variational approach to large N theories and large N QFT at finite temperature see
    • For a Hartree-Fock variational approach to large N theories and large N QFT at finite temperature see, W.A. Bardeen, M. Moshe, Phys. Rev. D 28 (1983) 1372
    • (1983) Phys. Rev. D , vol.28 , pp. 1372
    • Bardeen, W.A.1    Moshe, M.2
  • 26
    • 4243177600 scopus 로고
    • The non-linear σ-model is discussed inthe spirit of this review in
    • The non-linear σ-model is discussed inthe spirit of this review inE. Brézin, J. Zinn-Justin, Phys. Rev. Lett. 36(1976) 691
    • (1976) Phys. Rev. Lett. , vol.36 , pp. 691
    • Brézin, E.1    Zinn-Justin, J.2
  • 28
    • 0002784239 scopus 로고
    • Lattice calculations of the non-linear σ model with the large N expansion are reported in and in [24]
    • Lattice calculations of the non-linear σ model with the large N expansion are reported in Campostrini, M. Rossi, P. Phys. Lett. B 242 (1990) 81 and in [24]
    • (1990) Phys. Lett. B , vol.242 , pp. 81
    • Campostrini, M.1    Rossi, P.2
  • 30
    • 0000708146 scopus 로고
    • The CP(N-1) model is discussed in two dimensions with the large N expansion in and in Refs. [26-29]
    • The CP(N-1) model is discussed in two dimensions with the large N expansion in Lüscher, M. Phys. Lett. 78B (1978) 465 and in Refs. [26-29]
    • (1978) Phys. Lett. , vol.78 B , pp. 465
    • Lüscher, M.1
  • 38
    • 0019931021 scopus 로고
    • Some finite size calculations are reported in and in Refs. [31-33]
    • Some finite size calculations are reported in Brézin, E. J. Physique (Paris) 43 (1982) 15 and in Refs. [31-33]
    • (1982) J. Physique (Paris) , vol.43 , pp. 15
    • Brézin, E.1
  • 42
    • 0014606639 scopus 로고
    • The parametric representation has been introduced in and in [35]
    • The parametric representation has been introduced in Schofield, P. Litster, J.D. Ho, J.T. Phys. Rev. Lett. 23 (1969) 1098 and in [35]
    • (1969) Phys. Rev. Lett. , vol.23 , pp. 1098
    • Schofield, P.1    Litster, J.D.2    Ho, J.T.3
  • 46
    • 0141675912 scopus 로고
    • A similar analysis in the case of theories renormalizable beyond perturbation theory (like the non-linear σ or Thirring models) is found in [37] Springer, Berlin 1975
    • Kyoto 1975, Proceedings, Lecture Notes In Physics, Springer, Berlin 1975, pp. 102-106. A similar analysis in the case of theories renormalizable beyond perturbation theory (like the non-linear σ or Thirring models) is found in [37]
    • (1975) Proceedings, Lecture Notes in Physics , pp. 102-106
    • Kyoto, A.1
  • 48
    • 0001332110 scopus 로고
    • 4 theory in d=4 dimensions see Ref [8] in and the review [39]
    • 4 theory in d=4 dimensions see Ref [8] in Wilson, K.G. Phys. Rev. D 6 (1972) 419 and the review [39]
    • (1972) Phys. Rev. D , vol.6 , pp. 419
    • Wilson, K.G.1
  • 55
    • 4243632539 scopus 로고
    • The bound on the Higgs mass is discussed in and in Refs. [46,47]
    • The bound on the Higgs mass is discussed in Dashen, R.F. Neuberger, H. Phys. Rev. Lett. 50 (1983) 1897 and in Refs. [46,47]
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1897
    • Dashen, R.F.1    Neuberger, H.2
  • 60
    • 0141787843 scopus 로고
    • DESY preprint 77/05, Jan
    • Symanzik, K. DESY preprint 77/05, Jan. 1977.
    • (1977)
    • Symanzik, K.1
  • 61
    • 0000738197 scopus 로고
    • Functional renormalization group has been discussed in the large N limit in and in Refs. [50,51]
    • Functional renormalization group has been discussed in the large N limit in Reuter, M. Tetradis, N. Wetterich, C. Nucl. Phys. B 401 (1993) 567 and in Refs. [50,51]
    • (1993) Nucl. Phys. B , vol.401 , pp. 567
    • Reuter, M.1    Tetradis, N.2    Wetterich, C.3
  • 64
    • 0000173037 scopus 로고    scopus 로고
    • Large-N critical behaviour of O(N)×O(m) spin models is considered in and in [53]
    • Large-N critical behaviour of O(N)×O(m) spin models is considered in Pelissetto, A. Rossi, P. Vicari, E. Nucl. Phys. B 607 (2001) 605 and in [53]
    • (2001) Nucl. Phys. B , vol.607 , pp. 605
    • Pelissetto, A.1    Rossi, P.2    Vicari, E.3
  • 67
    • 0009194538 scopus 로고
    • The non-linear σ model two-point functions and mass gap in dimension 2 have been studied by large N techniquesin
    • The non-linear σ model two-point functions and mass gap in dimension 2 have been studied by large N techniques inV.F. Müller, T. Raddatz, W. Rühl, Nucl. Phys. B 251 (1985) 212
    • (1985) Nucl. Phys. B , vol.251 , pp. 212
    • Müller, V.F.1    Raddatz, T.2    Rühl, W.3
  • 69
    • 0141675905 scopus 로고
    • The consistency of the 1/N expansion to all orders has been proven in see also Ref. [57] The method presented here is taken from Ref. [2]
    • The consistency of the 1/N expansion to all orders has been proven in Ya Aref'eva, I. Nissimov E.R. and Pacheva, S.J. Commun. Math. Phys. 71 (1980) 213, see also Ref. [57]. The method presented here is taken from Ref. [2]
    • (1980) Commun. Math. Phys. , vol.71 , pp. 213
    • Ya Aref'eva, I.1    Nissimov, E.R.2    Pacheva, S.J.3
  • 71
    • 0017960156 scopus 로고
    • At present the longest 1/N series for exponents and amplitudes are found in and Refs. [59-61]
    • At present the longest 1/N series for exponents and amplitudes are found in Kondor, I. Temesvari, T. J. Phys. Lett. (Paris) 39 (1978) L99 and Refs. [59-61]
    • (1978) J. Phys. Lett. (Paris) , vol.39
    • Kondor, I.1    Temesvari, T.2
  • 79
    • 0032565494 scopus 로고    scopus 로고
    • Results concerning the β-function at order 1/N in the massive theory renormalized at zero momentum have been reported in cond-mat/9711078
    • Results concerning the β-function at order 1/N in the massive theory renormalized at zero momentum have been reported in Pelissetto, A. Vicari, E. Nucl. Phys. B 519 (1998) 626; cond-mat/9711078.
    • (1998) Nucl. Phys. B , vol.519 , pp. 626
    • Pelissetto, A.1    Vicari, E.2
  • 80
    • 0032577751 scopus 로고    scopus 로고
    • In particular, a calculation of the dimensions of composite operators are reported and the consequences for thestability of the fixed point of the non-linear σ model discussed in hep-th/9710015
    • In particular, a calculation of the dimensions of composite operators are reported and the consequences for thestability of the fixed point of the non-linear σ model discussed inS.E. Derkachov, A.N. Manashov, Nucl. Phys. B522 (1998) 301; hep-th/9710015.
    • (1998) Nucl. Phys. B , vol.522 , pp. 301
    • Derkachov, S.E.1    Manashov, A.N.2
  • 83
    • 41349114791 scopus 로고    scopus 로고
    • 2) is given in cond-mat/0206098
    • 2) is given in Gracey, J.A. Phys. Rev. E 66 (2002) 027102; cond-mat/0206098.
    • (2002) Phys. Rev. E , vol.66 , pp. 027102
    • Gracey, J.A.1
  • 89
    • 36149006782 scopus 로고
    • A four-fermion interaction with U(1) chiral invariance was proposed by Nambu and Jona-Lasinio as a basic mechanism to generate nucleon, scalar and pseudo-scalar σ,π masses:
    • A four-fermion interaction with U(1) chiral invariance was proposed by Nambu and Jona-Lasinio as a basic mechanism to generate nucleon, scalar and pseudo-scalar σ,π masses: Nambu, Y. Jona-Lasinio, G. Phys. Rev. 122 (1961) 345.
    • (1961) Phys. Rev. , vol.122 , pp. 345
    • Nambu, Y.1    Jona-Lasinio, G.2
  • 90
    • 33750493372 scopus 로고
    • The difficulties connected with this approach (approximate treatment of Dyson-Schwinger equations without small parameter, non renormalizable theory with cut-off) have been partially solved, the 1/N expansion introduced and the existence of IR fixed points pointed out in and in Ref. [74]
    • The difficulties connected with this approach (approximate treatment of Dyson-Schwinger equations without small parameter, non renormalizable theory with cut-off) have been partially solved, the 1/N expansion introduced and the existence of IR fixed points pointed out in Wilson, K.G. Phys. Rev. D 7 (1973) 2911 and in Ref. [74]
    • (1973) Phys. Rev. D , vol.7 , pp. 2911
    • Wilson, K.G.1
  • 93
    • 0000318152 scopus 로고
    • Calculations of RG functions in dimensions 2 and 2+E have been reported in hep-th/9308073 and Refs. [77-79]
    • Calculations of RG functions in dimensions 2 and 2+E have been reported in Kivel, N.A. Stepanenko, A.S. Vasil'ev, A.N. Nucl. Phys. B 424 (1994) 619; hep-th/9308073 and Refs. [77-79]
    • (1994) Nucl. Phys. B , vol.424 , pp. 619
    • Kivel, N.A.1    Stepanenko, A.S.2    Vasil'ev, A.N.3
  • 97
    • 25744458134 scopus 로고
    • The semi-classical spectrum for d=2 in the large N limit of the GN model (with discrete chiral invariance) was obtained from soliton calculation in
    • The semi-classical spectrum for d=2 in the large N limit of the GN model (with discrete chiral invariance) was obtained from soliton calculation in Dashen, R. Hasslacher, B. Neveu, A. Phys. Rev. D 12 (1975) 2443.
    • (1975) Phys. Rev. D , vol.12 , pp. 2443
    • Dashen, R.1    Hasslacher, B.2    Neveu, A.3
  • 98
    • 0000526110 scopus 로고
    • This study as well as some additional considerations concerning the factorization of S matrix elements at order 1/N have led to a conjecture of the exact spectrum at N finite and also in Refs. [82,83]
    • This study as well as some additional considerations concerning the factorization of S matrix elements at order 1/N have led to a conjecture of the exact spectrum at N finite Zamolodchikov, A.B. Zamolodchikov, Al.B. Phys. Lett. 72B (1978) 481 and also in Refs. [82,83]
    • (1978) Phys. Lett. , vol.72 B , pp. 481
    • Zamolodchikov, A.B.1    Zamolodchikov, Al.B.2
  • 101
    • 0141787840 scopus 로고
    • The properties of the NJL model in two dimensions are discussed in Recent advances J.B. Zuber, R. Stora (Eds.) Les Houches, 1982, Elsevier Science Pub., Amsterdam
    • The properties of the NJL model in two dimensions are discussed in Lowenstein, J.H. Recent advances in: J.B. Zuber, R. Stora (Eds.), Field Theory and Statistical Mechanics, Les Houches, 1982, Elsevier Science Pub., Amsterdam 1984.
    • (1984) Field Theory and Statistical Mechanics
    • Lowenstein, J.H.1
  • 103
    • 19244367553 scopus 로고    scopus 로고
    • Approximate functional RG has also been used in hep-th/0007093
    • Approximate functional RG has also been used in Rosa, L. Vitale, P. Wetterich, C. Phys. Rev. Lett. 86 (2001) 958; hep-th/0007093.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 958
    • Rosa, L.1    Vitale, P.2    Wetterich, C.3
  • 109
    • 0033114665 scopus 로고    scopus 로고
    • The GN and GNY models are related to the physics of the top quark condensate. For a review see for instance hep-ph/9702381
    • The GN and GNY models are related to the physics of the top quark condensate. For a review see for instance Cvetic, G. Rev. Mod. Phys. 71 (1999) 513; hep-ph/9702381.
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 513
    • Cvetic, G.1
  • 110
    • 0001232502 scopus 로고
    • Further RG calculations concerning the GN and NJL models at d=4 can be found in and [93]
    • Further RG calculations concerning the GN and NJL models at d=4 can be found in Fishbane, P.M. Norton, R.E. Phys. Rev. D 48 (1993) 4924 and [93]
    • (1993) Phys. Rev. D , vol.48 , pp. 4924
    • Fishbane, P.M.1    Norton, R.E.2
  • 112
    • 4243953577 scopus 로고
    • The large N expansion of the GN model in d=3 has been discussed in: and [95]
    • The large N expansion of the GN model in d=3 has been discussed in: Rosenstein, B. Warr, B. Park, S.H. Phys. Rev. Lett. 62 (1989) 1433 and [95]
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 1433
    • Rosenstein, B.1    Warr, B.2    Park, S.H.3
  • 114
    • 13844316088 scopus 로고
    • For an early review on the large N expansion of the GN model in d=3 see
    • For an early review on the large N expansion of the GN model in d=3 see Rosenstein, B. Warr, B. Park, S.H. Phys. Rep. 205 (1991) 59.
    • (1991) Phys. Rep. , vol.205 , pp. 59
    • Rosenstein, B.1    Warr, B.2    Park, S.H.3
  • 115
    • 0141564471 scopus 로고
    • A number of 1=N calculations concerning the GN and NJL models have been reported hep-th/9410121
    • A number of 1=N calculations concerning the GN and NJL models have been reported J.A. Gracey, Phys. Lett. B342 (1995) 297; hep-th/9410121
    • (1995) Phys. Lett. B , vol.342 , pp. 297
    • Gracey, J.A.1
  • 117
    • 26744472652 scopus 로고    scopus 로고
    • (Erratum); hep-th/9406162
    • Gracey J.A. Phys. Rev. D 59 1999 109904. (Erratum); hep-th/9406162
    • (1999) Phys. Rev. D , vol.59 , pp. 109904
    • Gracey, J.A.1
  • 120
    • 0001800077 scopus 로고
    • hep-th/9305012
    • Gracey J.A. Phys. Lett. B 308 1993 65. 65, hep-th/9305012.
    • (1993) Phys. Lett. B , vol.308 , pp. 65
    • Gracey, J.A.1
  • 121
    • 36149006176 scopus 로고
    • A few references on the Schwinger model and its relation with the confinement problem: and Refs. [99-102]
    • A few references on the Schwinger model and its relation with the confinement problem: Schwinger, J. Phys. Rev. 128 (1962) 2425 and Refs. [99-102]
    • (1962) Phys. Rev. , vol.128 , pp. 2425
    • Schwinger, J.1
  • 126
    • 0040964308 scopus 로고
    • For the calculationof the QED RG β functioninthe MS scheme see
    • For the calculationof the QED RG β functioninthe MS scheme see S.G. Gorishny, A.L. Kataev, S.A. Larin,Phys. Lett. B 194 (1987) 429
    • (1987) Phys. Lett. B , vol.194 , pp. 429
    • Gorishny, S.G.1    Kataev, A.L.2    Larin, S.A.3
  • 128
    • 0001710088 scopus 로고
    • A few references on Schwinger or QED in the large N limit: hep-th/9309092
    • A few references on Schwinger or QED in the large N limit: J.A. Gracey, Phys. Lett. B 317 (1993) 415; hep-th/9309092
    • (1993) Phys. Lett. B , vol.317 , pp. 415
    • Gracey, J.A.1
  • 129
    • 0010876355 scopus 로고
    • hep-th/9312055 and Refs. [105,106]
    • Gracey J.A. Nucl. Phys. B 414 1994 614. hep-th/9312055 and Refs. [105,106].
    • (1994) Nucl. Phys. B , vol.414 , pp. 614
    • Gracey, J.A.1
  • 132
    • 0000039205 scopus 로고
    • An early calculation for dimension d=2+E in the Thirring model is found in
    • An early calculation for dimension d=2+E in the Thirring model is found in Hikami, S. Muta, T. Prog. Theor. Phys. 57 (1977) 785.
    • (1977) Prog. Theor. Phys. , vol.57 , pp. 785
    • Hikami, S.1    Muta, T.2
  • 133
    • 0000342955 scopus 로고
    • The Thirring model has been investigated for N large in hep-th/9411016; hep-lat/9806022
    • The Thirring model has been investigated for N large in Hands, S.J. Phys. Rev. D 51 (1995) 5816; hep-th/9411016; hep-lat/9806022.
    • (1995) Phys. Rev. D , vol.51 , pp. 5816
    • Hands, S.J.1
  • 134
    • 0001669413 scopus 로고    scopus 로고
    • Recent simulations concerning the 3D Thirring model are reported in hep-lat/9906008 and [110]
    • Recent simulations concerning the 3D Thirring model are reported in Hands, Simon Lucini, Biagio Phys. Lett. B 461 (1999) 263; hep-lat/9906008 and [110]
    • (1999) Phys. Lett. B , vol.461 , pp. 263
    • Hands, S.1    Lucini, B.2
  • 136
    • 35949034972 scopus 로고
    • Dynamical models are reviewed from the RG point of view in
    • Dynamical models are reviewed from the RG point of view in Hohenberg, P.C. Halperin, B.I. Rev. Mod. Phys. 49 (1977) 435.
    • (1977) Rev. Mod. Phys. , vol.49 , pp. 435
    • Hohenberg, P.C.1    Halperin, B.I.2
  • 137
    • 0000840262 scopus 로고
    • The dynamic action associated with the Langevin equation has been introduced in
    • The dynamic action associated with the Langevin equation has been introduced in: Martin, P.C. Siggia, E.D. Rose, H.A. Phys. Rev. A 8 (1978) 423.
    • (1978) Phys. Rev. A , vol.8 , pp. 423
    • Martin, P.C.1    Siggia, E.D.2    Rose, H.A.3
  • 138
    • 11744292436 scopus 로고
    • For an early discussion of the renormalization of dynamic theories in a field theory language see for example
    • For an early discussion of the renormalization of dynamic theories in a field theory language see for example De Dominicis, C. Peliti, L. Phys. Rev. B 18 (1978) 353.
    • (1978) Phys. Rev. B , vol.18 , pp. 353
    • De Dominicis, C.1    Peliti, L.2
  • 139
    • 2742571438 scopus 로고
    • The relation between supersymmetry and dissipative Langevin or Fokker-Planck equations have been shown in and Refs. [115-117]
    • The relation between supersymmetry and dissipative Langevin or Fokker-Planck equations have been shown in Witten, E. Nucl. Phys. B 188 (1981) 513 and Refs. [115-117]
    • (1981) Nucl. Phys. B , vol.188 , pp. 513
    • Witten, E.1
  • 143
    • 0007034258 scopus 로고
    • [FS18] In the discussion of the dissipative dynamics we follow
    • In the discussion of the dissipative dynamics we follow Zinn-Justin, J. Nucl. Phys. B 275 [FS18] (1986) 135.
    • (1986) Nucl. Phys. B , vol.275 , pp. 135
    • Zinn-Justin, J.1
  • 145
    • 0039463487 scopus 로고
    • The non-linear σ-model has been considered in
    • The non-linear σ-model has been considered in Bausch, R. Janssen, H.K. Yamazaki, Y. Z. Phys. B 37 (1980) 163.
    • (1980) Z. Phys. B , vol.37 , pp. 163
    • Bausch, R.1    Janssen, H.K.2    Yamazaki, Y.3
  • 146
    • 0037421125 scopus 로고    scopus 로고
    • Parts of this section are based on hep-th/0209045
    • Parts of this section are based on Moshe, M. Zinn-Justin, J. Nucl. Phys. B 648 (2003) 131; hep-th/0209045.
    • (2003) Nucl. Phys. B , vol.648 , pp. 131
    • Moshe, M.1    Zinn-Justin, J.2
  • 147
    • 4244003768 scopus 로고
    • On supersymmetric O(N) quantum field theory at large N see also in: and Refs. [123,124]
    • On supersymmetric O(N) quantum field theory at large N see also in: Suzuki, T. Phys. Rev. D 32 (1985) 1017 and Refs. [123,124]
    • (1985) Phys. Rev. D , vol.32 , pp. 1017
    • Suzuki, T.1
  • 150
    • 0001414297 scopus 로고
    • The phase structure of the O(N) symmetric, supersymmetric model in d=3 was studied in
    • The phase structure of the O(N) symmetric, supersymmetric model in d=3 was studied in Bardeen, W.A. Higashijima, K. Moshe, M. Nucl. Phys. B 250 (1985) 437.
    • (1985) Nucl. Phys. B , vol.250 , pp. 437
    • Bardeen, W.A.1    Higashijima, K.2    Moshe, M.3
  • 151
    • 0141558309 scopus 로고
    • Studies of the scalar O(N)×O(N) model in dimensions 3 and 4-E are found in and Ref. [127]
    • Studies of the scalar O(N)×O(N) model in dimensions 3 and 4-E are found in: Salomonson, P. Skagerstam, B.S. Phys. Lett. 155B (1985) 100 and Ref. [127]
    • (1985) Phys. Lett. , vol.155 B , pp. 100
    • Salomonson, P.1    Skagerstam, B.S.2
  • 153
    • 0141564466 scopus 로고
    • The O(N)×O(N) symmetric, supersymmetric model in d=3 was studied in
    • The O(N)×O(N) symmetric, supersymmetric model in d=3 was studied in Eyal, O. Moshe, M. Phys. Lett. B 178 (1986) 379.
    • (1986) Phys. Lett. B , vol.178 , pp. 379
    • Eyal, O.1    Moshe, M.2
  • 154
    • 0001719865 scopus 로고
    • The supersymmetric O(N) non linear σ model has been described in
    • The supersymmetric O(N) non linear σ model has been described in: Witten, E. Phys. Rev. D 16 (1977) 2991.
    • (1977) Phys. Rev. D , vol.16 , pp. 2991
    • Witten, E.1
  • 155
    • 0000534116 scopus 로고
    • The study of general two-dimensional supersymmetric non-linear σ models has been initiated in
    • The study of general two-dimensional supersymmetric non-linear σ models has been initiated in: Freedman, D.Z. Townsend, P.K. Nucl. Phys. B 177 (1981) 282.
    • (1981) Nucl. Phys. B , vol.177 , pp. 282
    • Freedman, D.Z.1    Townsend, P.K.2
  • 157
    • 27844437220 scopus 로고
    • The general four-loop β-function is given in: Phys. Lett. B 173 (1986) 423
    • The general four-loop β-function is given in: Marcus Grisaru, T. van de Ven, A.E.M. Zanon, D. Nucl. Phys. B 277 (1986) 409, Phys. Lett. B 173 (1986) 423.
    • (1986) Nucl. Phys. B , vol.277 , pp. 409
    • Marcus Grisaru, T.1    van de Ven, A.E.M.2    Zanon, D.3
  • 158
    • 0009463657 scopus 로고
    • Critical exponents of the supersymmetric non-linear σ model are calculated as 1=N expansions in:
    • Critical exponents of the supersymmetric non-linear σ model are calculated as 1=N expansions in: J.A. Gracey, Nucl. Phys. B 348 (1991) 737
    • (1991) Nucl. Phys. B , vol.348 , pp. 737
    • Gracey, J.A.1
  • 161
    • 0041154480 scopus 로고    scopus 로고
    • For other supersymmetric models see for instance hep-ph/9702304 and Ref. [135]
    • For other supersymmetric models see for instance Ferreira, P.M. Jack, I. Jones, D.R.T. Phys. Lett. B 399 (1997) 258; hep-ph/9702304 and Ref. [135]
    • (1997) Phys. Lett. B , vol.399 , pp. 258
    • Ferreira, P.M.1    Jack, I.2    Jones, D.R.T.3
  • 163
    • 0000003461 scopus 로고
    • The study of finite temperature quantum field theory has been initially motivated by the discussions of cosmological problemsRefs. [137,138]
    • The study of finite temperature quantum field theory has been initially motivated by the discussions of cosmological problems Kirznits D.A. JETP Lett. 15 (1972) 529 and Refs. [137,138]
    • (1972) JETP Lett. , vol.15 , pp. 529
    • Kirznits, D.A.1
  • 167
    • 0000695768 scopus 로고
    • The possibility of phase transitions in heavy ion collisions has generated additional interest and Refs. [140-142]
    • The possibility of phase transitions in heavy ion collisions has generated additional interest Bernard, C.W. Phys. Rev. D 9 (1974) 3312 and Refs. [140-142]
    • (1974) Phys. Rev. D , vol.9 , pp. 3312
    • Bernard, C.W.1
  • 171
    • 18044386863 scopus 로고
    • Among the various reviews and textbooks see, for example, and Refs. [144-147]
    • Among the various reviews and textbooks see, for example, Landsman, N.P. van Weert, C. Phys. Rep. 145 (1987) 141 and Refs. [144-147]
    • (1987) Phys. Rep. , vol.145 , pp. 141
    • Landsman, N.P.1    van Weert, C.2
  • 176
    • 0000782868 scopus 로고
    • RG equations in the context of finite temperature dimensional reduction are discussed in
    • RG equations in the context of finite temperature dimensional reduction are discussed in Landsman, N.P. Nucl. Phys. B 322 (1989) 498.
    • (1989) Nucl. Phys. B , vol.322 , pp. 498
    • Landsman, N.P.1
  • 177
    • 0141675903 scopus 로고    scopus 로고
    • SACLAY preprint-SPH-T-00-055; hep-ph 0005272
    • Zinn-Justin, J. SACLAY preprint-SPH-T-00-055; hep-ph 0005272.
    • Zinn-Justin, J.1
  • 178
    • 0000594441 scopus 로고
    • Early articles on dimensional reduction include and Refs. [151-154]
    • Early articles on dimensional reduction include Ginsparg, P. Nucl. Phys. B 170 (1980) 388 and Refs. [151-154]
    • (1980) Nucl. Phys. B , vol.170 , pp. 388
    • Ginsparg, P.1
  • 185
    • 0035974994 scopus 로고    scopus 로고
    • Numerical simulations concerning the NJL 2+1 model with U(1) chiral symmetry are reported in hep-lat/0107004
    • Numerical simulations concerning the NJL 2+1 model with U(1) chiral symmetry are reported in Hands, S.J. Kogut, J.B. Strouthos, C.G. Phys. Lett. B 515 (2001) 407; hep-lat/0107004.
    • (2001) Phys. Lett. B , vol.515 , pp. 407
    • Hands, S.J.1    Kogut, J.B.2    Strouthos, C.G.3
  • 186
    • 0001164981 scopus 로고
    • The thermodynamics of the Gross-Neveu and Nambu-Jona-Lasinio models at all temperatures and densities at d=2 for N→∞ is discussed and the existence of instantons responsible of the symmetry restoration is demonstrated in
    • The thermodynamics of the Gross-Neveu and Nambu-Jona-Lasinio models at all temperatures and densities at d=2 for N→∞ is discussed and the existence of instantons responsible of the symmetry restoration is demonstrated in Dashen, R.F. Ma, S.K. Rajaraman, R. Phys. Rev. D 11 (1975) 1499.
    • (1975) Phys. Rev. D , vol.11 , pp. 1499
    • Dashen, R.F.1    Ma, S.K.2    Rajaraman, R.3
  • 188
    • 0141787834 scopus 로고    scopus 로고
    • For a review see, for example, Proceedings of the International School of Subnuclear Phys, Erice World Scientific, Singapore; hep-ph/9610247
    • For a review see, for example, Shaposhnikov, M.E. Proceedings of the International School of Subnuclear Phys, Erice 1996, World Scientific, Singapore; hep-ph/9610247.
    • (1996)
    • Shaposhnikov, M.E.1
  • 189
    • 26344449579 scopus 로고
    • Finite temperature calculations in gauge theories are reported in and Refs. [161,162]
    • Finite temperature calculations in gauge theories are reported in Arnold, P. Zhai, C. Phys. Rev. D 51 (1995) 1906 and Refs. [161,162]
    • (1995) Phys. Rev. D , vol.51 , pp. 1906
    • Arnold, P.1    Zhai, C.2
  • 192
    • 0000621082 scopus 로고
    • The Schwinger model is solved in
    • The Schwinger model is solved in Smilga, A.V. Phys. Lett. B 278 (1992) 371.
    • (1992) Phys. Lett. B , vol.278 , pp. 371
    • Smilga, A.V.1
  • 193
    • 0001765003 scopus 로고
    • Early discussions and controversy on the breakdown of supersymmetry at finite temperature are found in and in [165]
    • Early discussions and controversy on the breakdown of supersymmetry at finite temperature are found in Girardelo, L. Grisaru, M.T. Salomonson, P. Nucl. Phys. B 178 (1981) 331 and in [165]
    • (1981) Nucl. Phys. B , vol.178 , pp. 331
    • Girardelo, L.1    Grisaru, M.T.2    Salomonson, P.3
  • 195
    • 0002227189 scopus 로고
    • Das A. Phys. A 158 1989 1
    • (1989) Phys. A , vol.158 , pp. 1
    • Das, A.1
  • 196
    • 4244180073 scopus 로고    scopus 로고
    • Restoration of broken internal symmetries were discussed in [arXiv:hep-ph/9702319] and references therein
    • Restoration of broken internal symmetries were discussed in Riotto, A. Senjanović, G. Phys. Rev. Lett. 79 (1997) 349 [arXiv:hep-ph/9702319] and references therein.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 349
    • Riotto, A.1    Senjanović, G.2
  • 197
    • 17044436920 scopus 로고    scopus 로고
    • The thermodynamics of supersymmetric gauge theories was studied. and references therein
    • The thermodynamics of supersymmetric gauge theories was studied. Fotopoulos, A. Taylor, T.R. Phys. Rev. D 59 (1999) 061701 and references therein.
    • (1999) Phys. Rev. D , vol.59 , pp. 061701
    • Fotopoulos, A.1    Taylor, T.R.2
  • 198
    • 0030576761 scopus 로고    scopus 로고
    • The minimal supersymmetric model at finite temperatures was discussed in and in Ref. [169]
    • The minimal supersymmetric model at finite temperatures was discussed in Espinosa, J.R. Nucl. Phys. B 475 (1996) 273 and in Ref. [169]
    • (1996) Nucl. Phys. B , vol.475 , pp. 273
    • Espinosa, J.R.1
  • 200
    • 0001130146 scopus 로고    scopus 로고
    • (Erratum)
    • Laine M. Nucl. Phys. B 548 1999 637. (Erratum)
    • (1999) Nucl. Phys. B , vol.548 , pp. 637
    • Laine, M.1
  • 202
    • 0042568863 scopus 로고
    • J. de Boer, & G. E. Uhlenbeck (Eds.), Amsterdam: North-Holland Publ
    • Huang K. Stud. Stat. Mech, II in: de Boer J. Uhlenbeck G.E. (Eds.) 1964 1 North-Holland Publ. Amsterdam
    • (1964) Stud. Stat. Mech, II , pp. 1
    • Huang, K.1
  • 217
    • 0030191291 scopus 로고    scopus 로고
    • The following sections are taken mainly from hep-th/9601080
    • The following sections are taken mainly from Eyal, G. Moshe, M. Nishigaki, S. Zinn-Justin, J. Nucl. Phys. B 470 (1996) 369; hep-th/9601080.
    • (1996) Nucl. Phys. B , vol.470 , pp. 369
    • Eyal, G.1    Moshe, M.2    Nishigaki, S.3    Zinn-Justin, J.4
  • 218
    • 0040393258 scopus 로고
    • For a review on matrix models and double scaling limit see
    • For a review on matrix models and double scaling limit see Di Francesco, P. Ginsparg, P. Zinn-Justin, J. Phys. Rep. 254 (1995) 1.
    • (1995) Phys. Rep. , vol.254 , pp. 1
    • Di Francesco, P.1    Ginsparg, P.2    Zinn-Justin, J.3
  • 219
    • 0002007858 scopus 로고
    • Previous references on the double scaling limit in vector models include
    • Previous references on the double scaling limit in vector models include A. Anderson, R.C. Myers, V. Perival, Phys. Lett. B 254 (1991) 89
    • (1991) Phys. Lett. B , vol.254 , pp. 89
    • Anderson, A.1    Myers, R.C.2    Perival, V.3
  • 226
    • 0000491241 scopus 로고
    • The d=1 matrix problem is discussed in and Refs. [195-197]
    • The d=1 matrix problem is discussed in Ginsparg, P. Zinn-Justin, J. Phys. Lett. B 240 (1990) 333 and Refs. [195-197]
    • (1990) Phys. Lett. B , vol.240 , pp. 333
    • Ginsparg, P.1    Zinn-Justin, J.2
  • 231
    • 0141564473 scopus 로고
    • Early large N calculation in zero and one dimensions are reported in
    • Early large N calculation in zero and one dimensions are reported in A.J. Bray, J. Stat. Phys. 11 (1974) 29
    • (1974) J. Stat. Phys. , vol.11 , pp. 29
    • Bray, A.J.1
  • 232
    • 0011497666 scopus 로고
    • and Ref. [199]
    • Bray A.J. J. Phys. A 7 1974 2144. and Ref. [199].
    • (1974) J. Phys. A , vol.7 , pp. 2144
    • Bray, A.J.1
  • 234
    • 30244523032 scopus 로고
    • References on tricritical behaviour and massless dilaton include and Refs. [201-204]
    • References on tricritical behaviour and massless dilaton include Bardeen, W.A. Moshe, M. Bander, M. Phys. Rev. Lett. 52 (1984) 1188 and Refs. [201-204]
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 1188
    • Bardeen, W.A.1    Moshe, M.2    Bander, M.3
  • 240
    • 0001978661 scopus 로고
    • The structure of the energy momentum tensor in renormalizable quantum field theories and a discussion of explicitand spontaneous breaking of scale invariance can be found in
    • The structure of the energy momentum tensor in renormalizable quantum field theories and a discussion of explicitand spontaneous breaking of scale invariance can be found in C.G. Callan, S. Colman, R. Jackiw, Annals of Phys.59 (1970) 42
    • (1970) Annals of Phys. , vol.59 , pp. 42
    • Callan, C.G.1    Colman, S.2    Jackiw, R.3
  • 242
    • 0000491785 scopus 로고
    • A general discussion on breaking of scale invariance is found in
    • A general discussion on breaking of scale invariance is found in Adler, S.L. Rev. Mod. Phys. 54 (1982) 729.
    • (1982) Rev. Mod. Phys. , vol.54 , pp. 729
    • Adler, S.L.1

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