메뉴 건너뛰기




Volumn 11, Issue 3, 2010, Pages 351-431

Borel and stokes nonperturbative phenomena in topological string theory and c = 1 matrix models

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77955226892     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-010-0044-5     Document Type: Article
Times cited : (160)

References (100)
  • 2
    • 0011619305 scopus 로고
    • Phases of the large N matrix model and nonperturbative effects in 2D gravity
    • David F.: Phases of the large N matrix model and nonperturbative effects in 2D gravity. Nucl. Phys. B 348, 507 (1991).
    • (1991) Nucl. Phys. B , vol.348 , pp. 507
    • David, F.1
  • 3
    • 6044269713 scopus 로고
    • Nonperturbative effects in matrix models and vacua of two-dimensional gravity
    • arXiv:hep-th/9212106
    • David F.: Nonperturbative effects in matrix models and vacua of two-dimensional gravity. Phys. Lett. B 302, 403 (1993) arXiv: hep-th/9212106.
    • (1993) Phys. Lett. B , vol.302 , pp. 403
    • David, F.1
  • 4
    • 77955227245 scopus 로고    scopus 로고
    • Shenker, S. H.: The strength of nonperturbative effects in string theory. In: Cargèse Workshop on Random Surfaces, Quantum Gravity and Strings (1990).
  • 5
    • 4244105778 scopus 로고
    • Combinatorics of boundaries in string theory
    • arXiv:hep-th/9407031
    • Polchinski J.: Combinatorics of boundaries in string theory. Phys. Rev. D 50, 6041 (1994) arXiv: hep-th/9407031.
    • (1994) Phys. Rev. D , vol.50 , pp. 6041
    • Polchinski, J.1
  • 6
    • 23144436409 scopus 로고    scopus 로고
    • Nonperturbative effects in matrix models and D-Branes
    • arXiv:hep-th/0306177
    • Alexandrov S. Yu., Kazakov V. A., Kutasov D.: Nonperturbative effects in matrix models and D-Branes. JHEP 0309, 057 (2003) arXiv: hep-th/0306177.
    • (2003) JHEP , vol.309 , pp. 057
    • Alexandrov, S.Y.1    Kazakov, V.A.2    Kutasov, D.3
  • 7
    • 0037064465 scopus 로고    scopus 로고
    • Matrix models, topological strings, and supersymmetric gauge theories
    • arXiv:hep-th/0206255
    • Dijkgraaf R., Vafa C.: Matrix models, topological strings, and supersymmetric gauge theories. Nucl. Phys. B 644, 3 (2002) arXiv: hep-th/0206255.
    • (2002) Nucl. Phys. B , vol.644 , pp. 3
    • Dijkgraaf, R.1    Vafa, C.2
  • 8
    • 11244311845 scopus 로고    scopus 로고
    • Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
    • arXiv:hep-th/ 0207096
    • Mariño M.: Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants. Commun. Math. Phys. 253, 25 (2004) arXiv: hep-th/ 0207096.
    • (2004) Commun. Math. Phys. , vol.253 , pp. 25
    • Mariño, M.1
  • 9
    • 23044455832 scopus 로고    scopus 로고
    • Matrix model as a mirror of Chern-Simons theory
    • arXiv:hep-th/0211098
    • Aganagic M., Klemm A., Mariño M., Vafa C.: Matrix model as a mirror of Chern-Simons theory. JHEP 0402, 010 (2004) arXiv: hep-th/0211098.
    • (2004) JHEP , vol.402 , pp. 010
    • Aganagic, M.1    Klemm, A.2    Mariño, M.3    Vafa, C.4
  • 10
    • 43049095770 scopus 로고    scopus 로고
    • Open string amplitudes and large-order behavior in topological string theory
    • arXiv:hep-th/0612127
    • Mariño M.: Open string amplitudes and large-order behavior in topological string theory. JHEP 0803, 060 (2008) arXiv: hep-th/0612127.
    • (2008) JHEP , vol.803 , pp. 060
    • Mariño, M.1
  • 12
    • 77955227005 scopus 로고    scopus 로고
    • Bouchard, V., Klemm, A., Mariño, M., Pasquetti, S.: Topological open strings on orbifolds, arXiv: 0807. 0597[hep-th].
  • 13
    • 77952876835 scopus 로고    scopus 로고
    • Nonperturbative effects and the large-order behavior of matrix models and topological strings
    • arXiv:0711.1954[hep-th]
    • Mariño M., Schiappa R., Weiss M.: Nonperturbative effects and the large-order behavior of matrix models and topological strings. Commun. Number Theor. Phys. 2, 349 (2008) arXiv: 0711. 1954[hep-th].
    • (2008) Commun. Number Theor. Phys. , vol.2 , pp. 349
    • Mariño, M.1    Schiappa, R.2    Weiss, M.3
  • 14
    • 66749133777 scopus 로고    scopus 로고
    • Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
    • arXiv:0805.3033[hep-th]
    • Mariño M.: Nonperturbative effects and nonperturbative definitions in matrix models and topological strings. JHEP 0812, 114 (2008) arXiv: 0805. 3033[hep-th].
    • (2008) JHEP , vol.812 , pp. 114
    • Mariño, M.1
  • 15
    • 77955231954 scopus 로고    scopus 로고
    • Mariño, M., Schiappa, R., Weiss, M.: Multi-instantons and multi-cuts. J. Math. Phys. (2010, in press). arXiv: 0809. 2619[hep-th].
  • 17
    • 22144489179 scopus 로고    scopus 로고
    • On the chemical potential of D-instantons in c = 0 noncritical string theory
    • arXiv:hep-th/0503199
    • Ishibashi N., Yamaguchi A.: On the chemical potential of D-instantons in c = 0 noncritical string theory. JHEP 0506, 082 (2005) arXiv: hep-th/0503199.
    • (2005) JHEP , vol.506 , pp. 082
    • Ishibashi, N.1    Yamaguchi, A.2
  • 18
    • 33646859849 scopus 로고
    • Quantum field theory techniques in graphical enumeration
    • Bessis D., Itzykson C., Zuber J. B.: Quantum field theory techniques in graphical enumeration. Adv. Appl. Math. 1, 109 (1980).
    • (1980) Adv. Appl. Math. , vol.1 , pp. 109
    • Bessis, D.1    Itzykson, C.2    Zuber, J.B.3
  • 19
    • 77955231601 scopus 로고    scopus 로고
    • Eynard, B., Mariño, M.: A holomorphic and background independent partition function for matrix models and topological strings. arXiv: 0810. 4273[hep-th].
  • 20
    • 33847073369 scopus 로고    scopus 로고
    • Phase transitions, double-scaling limit, and topological strings
    • arXiv:hep-th/0606120
    • Caporaso N., Griguolo L., Mariño M., Pasquetti S., Seminara D.: Phase transitions, double-scaling limit, and topological strings. Phys. Rev. D 75, 046004 (2007) arXiv: hep-th/0606120.
    • (2007) Phys. Rev. D , vol.75 , pp. 046004
    • Caporaso, N.1    Griguolo, L.2    Mariño, M.3    Pasquetti, S.4    Seminara, D.5
  • 21
    • 42749098628 scopus 로고    scopus 로고
    • Black hole attractors and the topological string
    • arXiv:hep-th/0405146
    • Ooguri H., Strominger A., Vafa C.: Black hole attractors and the topological string. Phys. Rev. D 70, 106007 (2004) arXiv: hep-th/0405146.
    • (2004) Phys. Rev. D , vol.70 , pp. 106007
    • Ooguri, H.1    Strominger, A.2    Vafa, C.3
  • 22
    • 0013163563 scopus 로고
    • Perturbation series at large orders in quantum mechanics and field theories: Application to the problem of resummation
    • Zinn-Justin J.: Perturbation series at large orders in quantum mechanics and field theories: application to the problem of resummation. Phys. Rept. 70, 109 (1981).
    • (1981) Phys. Rept. , vol.70 , pp. 109
    • Zinn-Justin, J.1
  • 23
    • 33744760699 scopus 로고    scopus 로고
    • Topological gravity as large N topological gauge theory
    • arXiv:hep-th/9802016
    • Gopakumar R., Vafa C.: Topological gravity as large N topological gauge theory. Adv. Theor. Math. Phys. 2, 413 (1998) arXiv: hep-th/9802016.
    • (1998) Adv. Theor. Math. Phys. , vol.2 , pp. 413
    • Gopakumar, R.1    Vafa, C.2
  • 24
    • 77955230744 scopus 로고    scopus 로고
    • Gopakumar, R., Vafa, C.: M-theory and topological strings 1. arXiv: hep-th/9809187.
  • 25
    • 0000379578 scopus 로고
    • A nonperturbative solution of d = 1 string theory
    • Gross D. J., Miljkovic N.: A nonperturbative solution of d = 1 string theory. Phys. Lett. B 238, 217 (1990).
    • (1990) Phys. Lett. B , vol.238 , pp. 217
    • Gross, D.J.1    Miljkovic, N.2
  • 26
    • 33644667924 scopus 로고    scopus 로고
    • Nonperturbative effect in c = 1 noncritical string theory and Penner model
    • arXiv:hep-th/0512176
    • Matsuo Y.: Nonperturbative effect in c = 1 noncritical string theory and Penner model. Nucl. Phys. B 740, 222 (2006) arXiv: hep-th/0512176.
    • (2006) Nucl. Phys. B , vol.740 , pp. 222
    • Matsuo, Y.1
  • 27
    • 0347162275 scopus 로고
    • On gauge invariance and vacuum polarization
    • Schwinger J. H.: On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951).
    • (1951) Phys. Rev. , vol.82 , pp. 664
    • Schwinger, J.H.1
  • 28
    • 0012959190 scopus 로고
    • On Borel singularities in quantum field theory
    • Chadha S., Olesen P.: On Borel singularities in quantum field theory. Phys. Lett. B 72, 87 (1977).
    • (1977) Phys. Lett. B , vol.72 , pp. 87
    • Chadha, S.1    Olesen, P.2
  • 29
    • 7044255672 scopus 로고
    • Anharmonic oscillator 2: A study of perturbation theory in large order
    • Bender C. M., Wu T. T.: Anharmonic oscillator 2: a study of perturbation theory in large order. Phys. Rev. D 7, 1620 (1973).
    • (1973) Phys. Rev. D , vol.7 , pp. 1620
    • Bender, C.M.1    Wu, T.T.2
  • 30
    • 0012889381 scopus 로고
    • Large order expansion in perturbation theory
    • Collins J. C., Soper D. E.: Large order expansion in perturbation theory. Ann. Phys. 112, 209 (1978).
    • (1978) Ann. Phys. , vol.112 , pp. 209
    • Collins, J.C.1    Soper, D.E.2
  • 31
    • 77955230040 scopus 로고    scopus 로고
    • Dunne, G. V.: Heisenberg-Euler effective Lagrangians: basics and extensions. In: Ian Kogan Memorial Collection "From Fields to Strings: Circumnavigating Theoretical Physics" (2004). arXiv: hep-th/0406216.
  • 32
    • 33644940371 scopus 로고    scopus 로고
    • Kim S. P., Page D. N. (2006) Schwinger pair production in electric and magnetic fields. Phys. Rev. D 73, 065020 (2006) arXiv: hep-th/0301132.
  • 33
    • 0037203684 scopus 로고    scopus 로고
    • Closed form two loop Euler-Heisenberg Lagrangian in a selfdual background
    • arXiv:hep-th/0111134
    • Dunne G. V., Schubert C.: Closed form two loop Euler-Heisenberg Lagrangian in a selfdual background. Phys. Lett. B 526, 55 (2002) arXiv: hep-th/0111134.
    • (2002) Phys. Lett. B , vol.526 , pp. 55
    • Dunne, G.V.1    Schubert, C.2
  • 34
    • 23044474041 scopus 로고    scopus 로고
    • Two loop selfdual Euler-Heisenberg Lagrangians 1, real part and helicity amplitudes
    • arXiv:hep-th/0205004
    • Dunne G. V., Schubert C.: Two loop selfdual Euler-Heisenberg Lagrangians 1, real part and helicity amplitudes. JHEP 0208, 053 (2002) arXiv: hep-th/0205004.
    • (2002) JHEP , vol.208 , pp. 053
    • Dunne, G.V.1    Schubert, C.2
  • 35
    • 23044471665 scopus 로고    scopus 로고
    • Two loop selfdual Euler-Heisenberg Lagrangians 2, imaginary part and Borel analysis
    • arXiv:hep-th/0205005
    • Dunne G. V., Schubert C.: Two loop selfdual Euler-Heisenberg Lagrangians 2, imaginary part and Borel analysis. JHEP 0206, 042 (2002) arXiv: hep-th/0205005.
    • (2002) JHEP , vol.206 , pp. 042
    • Dunne, G.V.1    Schubert, C.2
  • 36
    • 0009561850 scopus 로고
    • Pair production in a variable external field (quasiclassical approximation)
    • Popov V. S.: Pair production in a variable external field (quasiclassical approximation). Sov. Phys. JETP 34, 709 (1972).
    • (1972) Sov. Phys. JETP , vol.34 , pp. 709
    • Popov, V.S.1
  • 37
    • 77955230619 scopus 로고    scopus 로고
    • Vonk, M.: A mini-course on topological strings. arXiv: hep-th/0504147.
  • 38
    • 0011625532 scopus 로고
    • Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
    • arXiv:hep-th/9309140
    • Bershadsky M., Cecotti S., Ooguri H., Vafa C.: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Commun. Math. Phys. 165, 311 (1994) arXiv: hep-th/9309140.
    • (1994) Commun. Math. Phys. , vol.165 , pp. 311
    • Bershadsky, M.1    Cecotti, S.2    Ooguri, H.3    Vafa, C.4
  • 39
    • 0010768747 scopus 로고
    • c = 1 String as the Topological Theory of the Conifold
    • arXiv:hep-th/9506122
    • Ghoshal D., Vafa C.: c = 1 String as the Topological Theory of the Conifold. Nucl. Phys. B 453, 121 (1995) arXiv: hep-th/9506122.
    • (1995) Nucl. Phys. B , vol.453 , pp. 121
    • Ghoshal, D.1    Vafa, C.2
  • 40
    • 77955227480 scopus 로고    scopus 로고
    • Klebanov, I. R.: String theory in two-dimensions. In: Trieste Spring School on string theory and quantum gravity (1991). arXiv: hep-th/9108019.
  • 41
    • 77955229794 scopus 로고    scopus 로고
    • Klemm, A., Zaslow, E.: Local mirror symmetry at higher genus. arXiv: hep-th/9906046.
  • 42
    • 79551488638 scopus 로고    scopus 로고
    • M-theory, topological strings and spinning black holes
    • arXiv:hep-th/9910181
    • Katz S., Klemm A., Vafa C.: M-theory, topological strings and spinning black holes. Adv. Theor. Math. Phys. 3, 1445 (1999) arXiv: hep-th/9910181.
    • (1999) Adv. Theor. Math. Phys. , vol.3 , pp. 1445
    • Katz, S.1    Klemm, A.2    Vafa, C.3
  • 43
    • 13444254226 scopus 로고
    • One-dimensional string theory on a circle
    • Gross D. J., Klebanov I. R.: One-dimensional string theory on a circle. Nucl. Phys. B 344, 475 (1990).
    • (1990) Nucl. Phys. B , vol.344 , pp. 475
    • Gross, D.J.1    Klebanov, I.R.2
  • 44
    • 77955230863 scopus 로고    scopus 로고
    • Gopakumar, R., Vafa, C.: M-theory and topological strings 2. arXiv: hep-th/9812127.
  • 45
    • 0033614220 scopus 로고    scopus 로고
    • Counting higher genus curves in a Calabi-Yau manifold
    • arXiv:hep-th/9808131
    • Mariño M., Moore G. W.: Counting higher genus curves in a Calabi-Yau manifold. Nucl. Phys. B 543, 592 (1999) arXiv: hep-th/9808131.
    • (1999) Nucl. Phys. B , vol.543 , pp. 592
    • Mariño, M.1    Moore, G.W.2
  • 46
    • 0034364921 scopus 로고    scopus 로고
    • Hodge integrals and Gromov-Witten theory
    • arXiv:math/9810173
    • Faber C., Pandharipande R.: Hodge integrals and Gromov-Witten theory. Invent. Math. 139, 173 (2000) arXiv: math/9810173.
    • (2000) Invent. Math. , vol.139 , pp. 173
    • Faber, C.1    Pandharipande, R.2
  • 47
    • 79551491388 scopus 로고    scopus 로고
    • Gopakumar R., Vafa C. (1999) On the gauge theory/geometry correspondence. Adv. Theor. Math. Phys. 3, 1415 (1999) arXiv: hep-th/9811131.
  • 48
    • 0001753344 scopus 로고
    • Chern-Simons gauge theory as a string theory
    • arXiv:hep-th/9207094
    • Witten E.: Chern-Simons gauge theory as a string theory. Prog. Math. 133, 637 (1995) arXiv: hep-th/9207094.
    • (1995) Prog. Math. , vol.133 , pp. 637
    • Witten, E.1
  • 50
    • 77955230554 scopus 로고    scopus 로고
    • Mariño, M.: Les Houches lectures on matrix models and topological strings. arXiv: hep-th/0410165.
  • 51
    • 67650829957 scopus 로고    scopus 로고
    • Invariants of algebraic curves and topological expansion
    • arXiv:math-ph/0702045
    • Eynard B., Orantin N.: Invariants of algebraic curves and topological expansion. Commun. Number Theor. Phys. 1, 347 (2007) arXiv: math-ph/0702045.
    • (2007) Commun. Number Theor. Phys. , vol.1 , pp. 347
    • Eynard, B.1    Orantin, N.2
  • 52
    • 77955227568 scopus 로고    scopus 로고
    • Eynard, B., Orantin, N.: Algebraic methods in random matrices and enumerative geometry. arXiv: 0811. 3531[math-ph].
  • 53
    • 0002673271 scopus 로고
    • The volume of a compact Lie group
    • Macdonald I. G.: The volume of a compact Lie group. Invent. Math. 56, 93 (1980).
    • (1980) Invent. Math. , vol.56 , pp. 93
    • Macdonald, I.G.1
  • 54
    • 84972538864 scopus 로고
    • Perturbative series and the moduli space of Riemann surfaces
    • Penner R. C.: Perturbative series and the moduli space of Riemann surfaces. J. Differ. Geom. 27, 35 (1988).
    • (1988) J. Differ. Geom. , vol.27 , pp. 35
    • Penner, R.C.1
  • 55
    • 77955230315 scopus 로고    scopus 로고
    • Distler, J., Vafa, C.: The Penner model and d = 1 string theory. In: Cargèse workshop on random surfaces, quantum gravity and strings (1990).
  • 56
    • 0001509680 scopus 로고
    • Critical matrix model at c = 1
    • Distler J., Vafa C.: Critical matrix model at c = 1. Mod. Phys. Lett. A 6, 259 (1991).
    • (1991) Mod. Phys. Lett. A , vol.6 , pp. 259
    • Distler, J.1    Vafa, C.2
  • 58
    • 0001706475 scopus 로고
    • Generalized Penner models to all genera
    • arXiv:hep-th/9403024
    • Ambjørn J., Kristjansen C. F., Makeenko Yu.: Generalized Penner models to all genera. Phys. Rev. D 50, 5193 (1994) arXiv: hep-th/9403024.
    • (1994) Phys. Rev. D , vol.50 , pp. 5193
    • Ambjørn, J.1    Kristjansen, C.F.2    Makeenko, Y.3
  • 59
    • 27144547045 scopus 로고    scopus 로고
    • Chern-Simons theory and topological strings
    • arXiv:hep-th/0406005
    • Mariño M.: Chern-Simons theory and topological strings. Rev. Mod. Phys. 77, 675 (2005) arXiv: hep-th/0406005.
    • (2005) Rev. Mod. Phys. , vol.77 , pp. 675
    • Mariño, M.1
  • 60
    • 2942750468 scopus 로고    scopus 로고
    • Soft matrix models and Chern-Simons partition functions
    • arXiv:hep-th/0212128
    • Tierz M.: Soft matrix models and Chern-Simons partition functions. Mod. Phys. Lett. A 19, 1365 (2004) arXiv: hep-th/0212128.
    • (2004) Mod. Phys. Lett. A , vol.19 , pp. 1365
    • Tierz, M.1
  • 61
    • 77955229946 scopus 로고    scopus 로고
    • Aganagic, M., Vafa, C.: Mirror symmetry, D-Branes and counting holomorphic discs. arXiv: hep-th/0012041.
  • 62
    • 0036345114 scopus 로고    scopus 로고
    • Disk instantons, mirror symmetry and the duality web
    • arXiv:hep-th/0105045
    • Aganagic M., Klemm A., Vafa C.: Disk instantons, mirror symmetry and the duality web. Z. Naturforsch. A 57, 1 (2002) arXiv: hep-th/0105045.
    • (2002) Z. Naturforsch. A , vol.57 , pp. 1
    • Aganagic, M.1    Klemm, A.2    Vafa, C.3
  • 63
    • 77955231525 scopus 로고    scopus 로고
    • Fateev, V., Zamolodchikov, A. B., Zamolodchikov, A. B.: Boundary Liouville field theory I: boundary state and boundary two-point function. arXiv: hep-th/0001012.
  • 64
    • 77955231024 scopus 로고    scopus 로고
    • Zamolodchikov, A. B., Zamolodchikov, A. B.: Liouville field theory on a pseudosphere. arXiv: hep-th/0101152.
  • 65
    • 33744725263 scopus 로고    scopus 로고
    • Bulk-boundary propagator in Liouville theory on a disc
    • arXiv:hep-th/0108093
    • Hosomichi K.: Bulk-boundary propagator in Liouville theory on a disc. JHEP 0111, 044 (2001) arXiv: hep-th/0108093.
    • (2001) JHEP , vol.111 , pp. 044
    • Hosomichi, K.1
  • 66
    • 77955232453 scopus 로고    scopus 로고
    • Martinec, E. J.: The annular report on non-critical string theory. arXiv: hep-th/0305148.
  • 67
    • 23044440216 scopus 로고    scopus 로고
    • Branes, rings and matrix models in minimal (Super)String Theory
    • arXiv:hep-th/0312170
    • Seiberg N., Shih D.: Branes, rings and matrix models in minimal (Super)String Theory. JHEP 0402, 021 (2004) arXiv: hep-th/0312170.
    • (2004) JHEP , vol.402 , pp. 021
    • Seiberg, N.1    Shih, D.2
  • 68
    • 19344370867 scopus 로고    scopus 로고
    • Time-dependent backgrounds of 2D string theory: Nonperturbative effects
    • arXiv:hep-th/0412223
    • Alexandrov S. Y., Kostov I. K.: Time-dependent backgrounds of 2D string theory: nonperturbative effects. JHEP 0502, 023 (2005) arXiv: hep-th/0412223.
    • (2005) JHEP , vol.502 , pp. 023
    • Alexandrov, S.Y.1    Kostov, I.K.2
  • 69
    • 23044486615 scopus 로고    scopus 로고
    • D-Branes and complex curves in c = 1 string theory
    • arXiv:hep-th/0403116
    • Alexandrov S.: D-Branes and complex curves in c = 1 string theory. JHEP 0405, 025 (2004) arXiv: hep-th/0403116.
    • (2004) JHEP , vol.405 , pp. 025
    • Alexandrov, S.1
  • 70
    • 77955228369 scopus 로고    scopus 로고
    • Kazakov, V. A., Kostov, I. K.: Instantons in non-critical strings from the two-matrix model. arXiv: hep-th/0403152.
  • 71
    • 9144254049 scopus 로고    scopus 로고
    • (m, n) ZZ Branes and the c = 1 Matrix Model
    • arXiv:hep-th/0310135
    • Alexandrov S.: (m, n) ZZ Branes and the c = 1 Matrix Model. Phys. Lett. B 604, 115 (2004) arXiv: hep-th/0310135.
    • (2004) Phys. Lett. B , vol.604 , pp. 115
    • Alexandrov, S.1
  • 72
    • 34247877695 scopus 로고    scopus 로고
    • Large N gauge theories and topological cigars
    • arXiv:hep-th/0611016
    • Bertoldi G., Hollowood T. J.: Large N gauge theories and topological cigars. JHEP 0704, 078 (2007) arXiv: hep-th/0611016.
    • (2007) JHEP , vol.704 , pp. 078
    • Bertoldi, G.1    Hollowood, T.J.2
  • 73
    • 77955230968 scopus 로고    scopus 로고
    • Adamchik, V. S.: Contributions to the theory of the Barnes function. arXiv: math/0308086[math. CA].
  • 76
    • 0002596327 scopus 로고    scopus 로고
    • The Devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
    • Boyd J. P.: The Devil's invention: asymptotic, superasymptotic and hyperasymptotic series. Acta Appl. Math. 56, 1 (1999).
    • (1999) Acta Appl. Math. , vol.56 , pp. 1
    • Boyd, J.P.1
  • 77
    • 0000724251 scopus 로고
    • Hyperasymptotics for integrals with saddles
    • Berry M. V., Howls C. J.: Hyperasymptotics for integrals with saddles. Proc. R. Soc. Lond. A 434, 657 (1991).
    • (1991) Proc. R. Soc. Lond. A , vol.434 , pp. 657
    • Berry, M.V.1    Howls, C.J.2
  • 78
    • 0345740992 scopus 로고
    • Error bounds for the method of steepest descents
    • Boyd W. G. C.: Error bounds for the method of steepest descents. Proc. R. Soc. Lond. A 440, 493 (1993).
    • (1993) Proc. R. Soc. Lond. A , vol.440 , pp. 493
    • Boyd, W.G.C.1
  • 79
    • 77955231107 scopus 로고    scopus 로고
    • Friot, S., Greynat, D.: Non-perturbative asymptotic improvement of perturbation theory and Mellin-Barnes representation. arXiv: 0907. 5593[hep-th].
  • 81
    • 33746419492 scopus 로고
    • Gamma function asymptotics by an extension of the method of steepest descents
    • Boyd W. G. C.: Gamma function asymptotics by an extension of the method of steepest descents. Proc. R. Soc. Lond. A 447, 609 (1994).
    • (1994) Proc. R. Soc. Lond. A , vol.447 , pp. 609
    • Boyd, W.G.C.1
  • 82
    • 0039402679 scopus 로고
    • Infinitely many stokes smoothings in the gamma function
    • Berry M. V.: Infinitely many stokes smoothings in the gamma function. Proc. R. Soc. Lond. A 434, 465 (1991).
    • (1991) Proc. R. Soc. Lond. A , vol.434 , pp. 465
    • Berry, M.V.1
  • 83
    • 77955230279 scopus 로고    scopus 로고
    • Koshkin, S.: Quantum Barnes function as the partition function of the resolved conifold. arXiv: 0710. 2929[math. AG].
  • 84
    • 23044501159 scopus 로고    scopus 로고
    • Exact vs. semiclassical target space of the minimal string
    • arXiv:hep-th/0408039
    • Maldacena J. M., Moore G. W., Seiberg N., Shih D.: Exact vs. semiclassical target space of the minimal string. JHEP 0410, 020 (2004) arXiv: hep-th/0408039.
    • (2004) JHEP , vol.410 , pp. 020
    • Maldacena, J.M.1    Moore, G.W.2    Seiberg, N.3    Shih, D.4
  • 85
    • 67649553450 scopus 로고    scopus 로고
    • Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence
    • arXiv:0802.1788[math-ph]
    • Eynard B.: Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence. JHEP 0903, 003 (2009) arXiv: 0802. 1788[math-ph].
    • (2009) JHEP , vol.903 , pp. 003
    • Eynard, B.1
  • 86
    • 0002360911 scopus 로고
    • Uniform asymptotic smoothing of Stokes' discontinuities
    • Berry M. V.: Uniform asymptotic smoothing of Stokes' discontinuities. Proc. R. Soc. Lond. A 422, 7 (1989).
    • (1989) Proc. R. Soc. Lond. A , vol.422 , pp. 7
    • Berry, M.V.1
  • 87
    • 0345740991 scopus 로고    scopus 로고
    • On the non-universality of the error function in the smoothing of stokes discontinuities
    • Chapman S. J.: On the non-universality of the error function in the smoothing of stokes discontinuities. Proc. R. Soc. Lond. A 452, 2225 (1996).
    • (1996) Proc. R. Soc. Lond. A , vol.452 , pp. 2225
    • Chapman, S.J.1
  • 88
    • 0034730267 scopus 로고    scopus 로고
    • Breakdown of universality in multicut matrix models
    • arXiv:cond-mat/0003324
    • Bonnet G., David F., Eynard B.: Breakdown of universality in multicut matrix models. J. Phys. A 33, 6739 (2000) arXiv: cond-mat/0003324.
    • (2000) J. Phys. A , vol.33 , pp. 6739
    • Bonnet, G.1    David, F.2    Eynard, B.3
  • 89
    • 1542407751 scopus 로고    scopus 로고
    • The dilogarithm function for complex argument
    • Maximon L. C.: The dilogarithm function for complex argument. Proc. R. Soc. Lond. A 459, 2807 (2003).
    • (2003) Proc. R. Soc. Lond. A , vol.459 , pp. 2807
    • Maximon, L.C.1
  • 90
    • 79952531395 scopus 로고    scopus 로고
    • An Efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
    • arXiv:math/0702243
    • Vepštas L.: An Efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions. Numer. Algorithm 47, 211 (2008) arXiv: math/0702243.
    • (2008) Numer. Algorithm , vol.47 , pp. 211
    • Vepštas, L.1
  • 91
    • 4243355692 scopus 로고    scopus 로고
    • Summing up D-Instantons
    • arXiv:hep-th/9608079
    • Ooguri H., Vafa C.: Summing up D-Instantons. Phys. Rev. Lett. 77, 3296 (1996) arXiv: hep-th/9608079.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 3296
    • Ooguri, H.1    Vafa, C.2
  • 92
    • 77955229861 scopus 로고    scopus 로고
    • Collinucci, A., Soler, P., Uranga, A. M.: Nonperturbative effects and wall-crossing from topological strings. arXiv: 0904. 1133[hep-th].
  • 93
    • 0001636356 scopus 로고
    • The partition function of 2D string theory
    • arXiv:hep-th/9208031
    • Dijkgraaf R., Moore G. W., Plesser R.: The partition function of 2D string theory. Nucl. Phys. B 394, 356 (1993) arXiv: hep-th/9208031.
    • (1993) Nucl. Phys. B , vol.394 , pp. 356
    • Dijkgraaf, R.1    Moore, G.W.2    Plesser, R.3
  • 94
    • 0037016911 scopus 로고    scopus 로고
    • A matrix model for the two-dimensional black hole
    • arXiv:hep-th/0101011
    • Kazakov V., Kostov I. K., Kutasov D.: A matrix model for the two-dimensional black hole. Nucl. Phys. B 622, 141 (2002) arXiv: hep-th/0101011.
    • (2002) Nucl. Phys. B , vol.622 , pp. 141
    • Kazakov, V.1    Kostov, I.K.2    Kutasov, D.3
  • 95
    • 77955231727 scopus 로고    scopus 로고
    • Sauzin, D.: Resurgent functions and splitting problems. arXiv: 0706. 0137 [math. DS].
  • 96
    • 0001664092 scopus 로고    scopus 로고
    • BPS states of curves in Calabi-Yau Threefolds
    • arXiv:math/0009025
    • Bryan J., Pandharipande R.: BPS states of curves in Calabi-Yau Threefolds. Geom. Topol. 5, 287 (2001) arXiv: math/0009025.
    • (2001) Geom. Topol. , vol.5 , pp. 287
    • Bryan, J.1    Pandharipande, R.2
  • 97
    • 0035646410 scopus 로고    scopus 로고
    • Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds
    • arXiv:math/9911056
    • Bryan J., Katz S., Leung N. C.: Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds. J. Algebraic Geom. 10, 549 (2001) arXiv: math/9911056.
    • (2001) J. Algebraic Geom. , vol.10 , pp. 549
    • Bryan, J.1    Katz, S.2    Leung, N.C.3
  • 98
    • 33644805440 scopus 로고    scopus 로고
    • The local Gromov-Witten invariants of configurations of rational curves
    • arXiv:math/0506488
    • Karp D., Liu C.-C. M., Mariño M.: The local Gromov-Witten invariants of configurations of rational curves. Geom. Topol. 10, 115 (2006) arXiv: math/0506488.
    • (2006) Geom. Topol. , vol.10 , pp. 115
    • Karp, D.1    Liu, C.-C.M.2    Mariño, M.3
  • 99
    • 33846151394 scopus 로고    scopus 로고
    • Branes, black holes and topological strings on toric Calabi-Yau manifolds
    • arXiv:hep-th/0512245
    • Aganagic M., Jafferis D., Saulina N.: Branes, black holes and topological strings on toric Calabi-Yau manifolds. JHEP 0612, 018 (2006) arXiv: hep-th/0512245.
    • (2006) JHEP , vol.612 , pp. 018
    • Aganagic, M.1    Jafferis, D.2    Saulina, N.3
  • 100
    • 58149277506 scopus 로고    scopus 로고
    • Integrability of the holomorphic anomaly equations
    • arXiv:0809.1674[hep-th]
    • Haghighat B., Klemm A., Rauch M.: Integrability of the holomorphic anomaly equations. JHEP 0810, 097 (2008) arXiv: 0809. 1674[hep-th].
    • (2008) JHEP , vol.810 , pp. 097
    • Haghighat, B.1    Klemm, A.2    Rauch, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.