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Volumn 3, Issue 2, 2009, Pages 363-443

Exact results for perturbative Chern-Simons theory with complex gauge group

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EID: 77952552744     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2009.v3.n2.a4     Document Type: Article
Times cited : (169)

References (59)
  • 1
    • 33646175970 scopus 로고    scopus 로고
    • Asymptotics of the quantum invariants for surgeries on the figure 8 knot
    • J.E. Andersen and S.K. Hansen, Asymptotics of the quantum invariants for surgeries on the figure 8 knot, J. Knot Theory Ramifications 15(4) (2006), 479-548.
    • (2006) J. Knot Theory Ramifications , vol.15 , Issue.4 , pp. 479-548
    • Andersen, J.E.1    Hansen, S.K.2
  • 5
    • 0342885396 scopus 로고
    • Perturbative expansion of Chern-Simons theory with noncompact gauge group
    • D. Bar-Natan and E. Witten, Perturbative expansion of Chern-Simons theory with noncompact gauge group, Commun. Math. Phys. 141 (1991), 423.
    • (1991) Commun. Math. Phys. , vol.141 , pp. 423
    • Bar-Natan, D.1    Witten, E.2
  • 6
    • 33744769996 scopus 로고
    • Deformation theory and quantization. 1. Deformations of symplectic structures
    • F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization. 1. Deformations of symplectic structures, Annals Phys. 111 (1978), 61.
    • (1978) Annals Phys , vol.111 , pp. 61
    • Bayen, F.1    Flato, M.2    Fronsdal, C.3    Lichnerowicz, A.4    Sternheimer, D.5
  • 7
    • 33747186382 scopus 로고    scopus 로고
    • On motives associated to graph polynomials, Commun
    • math/0510011
    • S. Bloch, H. Esnault and D. Kreimer, On motives associated to graph polynomials, Commun. Math. Phys. 267 (2006), 181-225, math/0510011.
    • (2006) Math. Phys , vol.267 , pp. 181-225
    • Bloch, S.1    Esnault, H.2    Kreimer, D.3
  • 8
    • 0002576110 scopus 로고
    • Plane curves associated to character varieties of 3-manifolds
    • D. Cooper, M. Culler, H. Gillet, D. Long and P. Shalen, Plane curves associated to character varieties of 3-manifolds, Invent. Math. 118 (1994), 47-84.
    • (1994) Invent. Math. , vol.118 , pp. 47-84
    • Cooper, D.1    Culler, M.2    Gillet, H.3    Long, D.4    Shalen, P.5
  • 9
    • 0030524462 scopus 로고    scopus 로고
    • Remarks on the A-polynomial of a knot
    • D. Cooper and D. Long, Remarks on the A-polynomial of a knot, J. Knot Theory Ramifications 5(5) (1996), 609-628.
    • (1996) J. Knot Theory Ramifications , vol.5 , Issue.5 , pp. 609-628
    • Cooper, D.1    Long, D.2
  • 10
    • 85039674218 scopus 로고    scopus 로고
    • Resurgence of 1-dimensional sums of sum-product type, in preparation
    • O. Costin and S. Garoufalidis, Resurgence of 1-dimensional sums of sum-product type, in preparation.
    • Costin, O.1    Garoufalidis, S.2
  • 12
    • 84865990686 scopus 로고    scopus 로고
    • Current-like variables in massive and massless integrable models, in Quantum groups and their applications in physics (Varenna 1994)
    • Proceedings of the International School of Physics Enrico Fermi 127, IOS Amsterdam, hep-th/9408041
    • L. D. Faddeev, Current-like variables in massive and massless integrable models, in Quantum groups and their applications in physics (Varenna 1994), 117-135, Proceedings of the International School of Physics Enrico Fermi, 127, IOS, Amsterdam, 1996, hep-th/ 9408041.
    • (1996) , vol.117-135
    • Faddeev, L.D.1
  • 14
    • 0000561791 scopus 로고    scopus 로고
    • Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
    • hep-th/0006156
    • L. D. Faddeev, R. M. Kashaev and A. Y. Volkov, Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality, Commun. Math. Phys. 219 (2001), 199-219, hep-th/0006156.
    • (2001) Commun. Math. Phys. , vol.219 , pp. 199-219
    • Faddeev, L.D.1    Kashaev, R.M.2    Volkov, A.Y.3
  • 15
    • 85039692740 scopus 로고    scopus 로고
    • Remarks on Chern-Simons theory, arXiv:0808.2507 [math.AT]
    • D. S. Freed, Remarks on Chern-Simons theory, arXiv:0808.2507 [math.AT].
    • Freed, D.S.1
  • 16
    • 17144362238 scopus 로고    scopus 로고
    • On the characteristic and deformation varieties of a knot
    • eds. C. Gordon, Y. Rieck, Geometry and Topology Publishing Coventry
    • S. Garoufalidis, On the characteristic and deformation varieties of a knot, eds. C. Gordon, Y. Rieck, in Geometry and Topology Monographs, 7, Geometry and Topology Publishing, Coventry, 2004, 291-309.
    • (2004) Geometry and Topology Monographs , vol.7 , pp. 291-309
    • Garoufalidis, S.1
  • 17
    • 44249116119 scopus 로고    scopus 로고
    • Asymptotics of q-difference equations
    • S. Garoufalidis and J. Geronimo, Asymptotics of q-difference equations, Contemp. Math. 416 (2006), 83-114.
    • (2006) Contemp. Math. , vol.416 , pp. 83-114
    • Garoufalidis, S.1    Geronimo, J.2
  • 18
    • 85039678402 scopus 로고    scopus 로고
    • Riemann-Hilbert approach to the asymptotics of 1-dimensional sums of Sum-Product type, in preparation
    • S. Garoufalidis and J. Geronimo, A Riemann-Hilbert approach to the asymptotics of 1-dimensional sums of Sum-Product type, in preparation.
    • Garoufalidis, S.1    Geronimo, J.A.2
  • 19
    • 79959825806 scopus 로고    scopus 로고
    • The pentagon relation for the quantum dilogarithm and quantized M0, 5
    • eds. Kapranov, M., Kolyada, S., Manin, Y.I., Moree, P., Potyagailo, L., Progr. Math, Birkḧauser, Basel, arXiv:0706.4054 [math.QA]
    • A. B. Goncharov, The pentagon relation for the quantum dilogarithm and quantized M0,5, in Geometry and dynamics of groups and spaces, eds. Kapranov, M., Kolyada, S., Manin, Y.I., Moree, P., Potyagailo, L., Progr. Math. 265, 415-428, Birkḧauser, Basel, 2008, arXiv:0706.4054 [math.QA].
    • (2008) Geometry and dynamics of groups and spaces , vol.265 , pp. 415-428
    • Goncharov, A.B.1
  • 20
    • 60349095467 scopus 로고    scopus 로고
    • Sequences of enumerative geometry: congruences and asymptotics
    • D. B. Gr̈unberg and P. Moree, Sequences of enumerative geometry: congruences and asymptotics. Exp. Math. 17(4) (2008), 409-426.
    • (2008) Exp. Math. , vol.17 , Issue.4 , pp. 409-426
    • Grünberg, D.B.1    Moree, P.2
  • 21
    • 17144388968 scopus 로고    scopus 로고
    • Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial
    • S. Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial, Commun. Math. Phys. 255, (2005), 577-627, hep-th/0306165.
    • (2005) Commun. Math. Phys. , vol.255 , pp. 577-627
    • Gukov, S.1
  • 22
    • 84865975844 scopus 로고    scopus 로고
    • SL(2, C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial, math/0608324
    • S. Gukov and H. Murakami, SL(2, C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial, (2006), math/0608324.
    • (2006)
    • Gukov, S.1    Murakami, H.2
  • 23
    • 85039691373 scopus 로고    scopus 로고
    • Branes and quantization, arXiv:0809.0305
    • S. Gukov and E. Witten, Branes and quantization, arXiv:0809.0305 [hep-th].
    • Gukov, S.1    Witten, E.2
  • 25
    • 0035974536 scopus 로고    scopus 로고
    • Hyperbolic structure arising from a knot invariant
    • math-ph/0105039
    • K. Hikami, Hyperbolic structure arising from a knot invariant, Int. J. Mod. Phys. A 16 (2001), 3309-3333, math-ph/0105039.
    • (2001) Int. J. Mod. Phys. A , vol.16 , pp. 3309-3333
    • Hikami, K.1
  • 26
    • 34248578237 scopus 로고    scopus 로고
    • Generalized volume conjecture and the A-polynomials: the Neumann-Zagier potential function as a classical limit of the partition function
    • K. Hikami, Generalized volume conjecture and the A-polynomials: the Neumann-Zagier potential function as a classical limit of the partition function, J. Geom. Phys. 57(9) (2007), 1895-1940.
    • (2007) J. Geom. Phys. , vol.57 , Issue.9 , pp. 1895-1940
    • Hikami, K.1
  • 27
    • 0009072969 scopus 로고
    • The self-duality equations on a riemann surface
    • N. Hitchin, The self-duality equations on a riemann surface, Proc. London Math. Soc. 55(3) (1987), 59-126.
    • (1987) Proc. London Math. Soc. , vol.55 , Issue.3 , pp. 59-126
    • Hitchin, N.1
  • 28
    • 0000356516 scopus 로고    scopus 로고
    • The hyperbolic volume of knots from the quantum dilogarithm
    • q-alg/9601025
    • R. M. Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997), 269-275, q-alg/9601025.
    • (1997) Lett. Math. Phys , vol.39 , pp. 269-275
    • Kashaev, R.M.1
  • 29
    • 33750026792 scopus 로고    scopus 로고
    • On the spectrum of Dehn twists in quantum Teichmuller theory
    • World Sci. Publ., River Edge, NJ math/0008148
    • R. M. Kashaev, On the spectrum of Dehn twists in quantum Teichmuller theory, in Physics and Combinatorics (Nagoya, 2000), World Sci. Publ., River Edge, NJ, 2001, (63-81), math/0008148.
    • (2001) Physics and Combinatorics (Nagoya, 2000) , Issue.63-81
    • Kashaev, R.M.1
  • 31
    • 0042704087 scopus 로고    scopus 로고
    • Deformation quantization of algebraic varieties
    • math/0106006
    • M. Kontsevich, Deformation quantization of algebraic varieties, Lett. Math. Phys. 56 (2006), 271-294, math/0106006.
    • (2006) Lett. Math. Phys. , vol.56 , pp. 271-294
    • Kontsevich, M.1
  • 32
    • 85039675959 scopus 로고    scopus 로고
    • Chern-Simons gauge theory: ten years after, hep-th/9905057
    • J. M. F. Labastida, Chern-Simons gauge theory: ten years after, (1999), hep-th/9905057.
    • (1999)
    • Labastida, J.M.F.1
  • 33
    • 0035645843 scopus 로고    scopus 로고
    • Period functions for Maass wave forms
    • J. Lewis, D. Zagier, Period functions for Maass wave forms. I, Ann. Math. 153 (2001), 191-258.
    • (2001) I, Ann. Math. , vol.153 , pp. 191-258
    • Lewis, J.1    Zagier, D.2
  • 34
    • 27144547045 scopus 로고    scopus 로고
    • Chern-Simons theory and topological strings
    • hep-th/0406005
    • M. Marino, Chern-Simons theory and topological strings, Rev. Mod. Phys. 77 (2005), 675, hep-th/0406005.
    • (2005) Rev. Mod. Phys , vol.77 , pp. 675
    • Marino, M.1
  • 35
    • 0002249763 scopus 로고
    • Hyperbolic geometry: the first 150 years
    • J. Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. 6 (1982), 9-24.
    • (1982) Bull. Amer. Math. Soc. , vol.6 , pp. 9-24
    • Milnor, J.1
  • 36
    • 0003297251 scopus 로고
    • Strong rigidity of locally symmetric spaces
    • G.D. Mostow, Strong rigidity of locally symmetric spaces, Ann. Math. Studies 78 (1973), 195 pp.
    • (1973) Ann. Math. Studies , vol.78 , pp. 195
    • Mostow, G.D.1
  • 38
    • 0346913205 scopus 로고    scopus 로고
    • Hamiltonian theories of the fractional quantum Hall effect
    • G. Murthy and R. Shankar, Hamiltonian theories of the fractional quantum Hall effect, Rev. Mod. Phys. 75 (2003), 1101.
    • (2003) Rev. Mod. Phys. , vol.75 , pp. 1101
    • Murthy, G.1    Shankar, R.2
  • 39
    • 4243068575 scopus 로고    scopus 로고
    • Extended Bloch group and the Cheeger-Chern- Simons class
    • W. D. Neumann, Extended Bloch group and the Cheeger-Chern- Simons class, Geom. Topol. 8 (2004), 413-474.
    • (2004) Geom. Topol. , vol.8 , pp. 413-474
    • Neumann, W.D.1
  • 40
    • 0033555096 scopus 로고    scopus 로고
    • Bloch invariants of hyperbolic 3-manifolds
    • W. D. Neumann and J. Yang, Bloch invariants of hyperbolic 3-manifolds, Duke Math. J. 96 (1999), 29-59.
    • (1999) Duke Math. J. , vol.96 , pp. 29-59
    • Neumann, W.D.1    Yang, J.2
  • 41
    • 0000459324 scopus 로고
    • Volumes of hyperbolic three-manifolds
    • W. D. Neumann and D. Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985), 397-332.
    • (1985) Topology , vol.24 , pp. 397-332
    • Neumann, W.D.1    Zagier, D.2
  • 42
    • 0039608500 scopus 로고    scopus 로고
    • Partially flat ideal triangulations of cusped hyperbolic 3-manifolds
    • C. Petronio and J.R.Weeks, Partially flat ideal triangulations of cusped hyperbolic 3-manifolds, Osaka J. Math. 37 (2000), 453-466.
    • (2000) Osaka J. Math. , vol.37 , pp. 453-466
    • Petronio, C.1    Weeks, J.R.2
  • 43
    • 0001743192 scopus 로고
    • Strong rigidity of Q-rank 1 lattices
    • G. Prasad, Strong rigidity of Q-rank 1 lattices, Invent. Math. 21 (1973), 255-286.
    • (1973) Invent. Math. , vol.21 , pp. 255-286
    • Prasad, G.1
  • 44
    • 13644276850 scopus 로고
    • Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
    • 19 [Erratum-ibid. B 430 (1994) 485], hep-th/9407087
    • N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994), 19 [Erratum-ibid. B 430 (1994) 485], hep-th/9407087.
    • (1994) Nucl. Phys. B , pp. 426
    • Seiberg, N.1    Witten, E.2
  • 46
    • 84966239529 scopus 로고
    • Three dimensional manifolds, kleinian groups, and hyperbolic geometry
    • W. P. Thurston, Three dimensional manifolds, kleinian groups, and hyperbolic geometry, Bull. Amer. Math. Soc. 6(3) (1982), 357-381.
    • (1982) Bull. Amer. Math. Soc. , vol.6 , Issue.3 , pp. 357-381
    • Thurston, W.P.1
  • 47
    • 0001182097 scopus 로고
    • Hyperbolic structures on 3-manifolds. I. Deformations of acylindrical manifolds
    • W. P. Thurston, Hyperbolic structures on 3-manifolds. I. Deformations of acylindrical manifolds, Ann. Math. 124(2) (1986), 203-246.
    • (1986) Ann. Math. , vol.124 , Issue.2 , pp. 203-246
    • Thurston, W.P.1
  • 49
    • 44049114062 scopus 로고
    • State-sum invariants of 3-manifolds and quantum 6j-symbols
    • V.G. Turaev and O.Yu. Viro, State-sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31 (1992), 865.
    • (1992) Topology , vol.31 , pp. 865
    • Turaev, V.G.1    Viro, O.Yu.2
  • 50
    • 22544469184 scopus 로고    scopus 로고
    • Noncommutative hypergeometry
    • math/0312084
    • A. Y. Volkov, Noncommutative hypergeometry, Commun. Math. Phys. 258(2) (2005), 257-273, math/0312084.
    • (2005) Commun. Math. Phys. , vol.258 , Issue.2 , pp. 257-273
    • Volkov, A.Y.1
  • 51
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989), 351-399.
    • (1989) Commun. Math. Phys. , vol.121 , pp. 351-399
    • Witten, E.1
  • 52
    • 0001930894 scopus 로고
    • Quantization of Chern-Simons gauge theory with complex gauge group
    • E. Witten, Quantization of Chern-Simons gauge theory with complex gauge group, Commun. Math. Phys. 137 (1991), 29.
    • (1991) Commun. Math. Phys. , vol.137 , pp. 29
    • Witten, E.1
  • 54
    • 0001271705 scopus 로고
    • The η-invariant of hyperbolic 3-manifolds
    • T. Yoshida, The η-invariant of hyperbolic 3-manifolds, Invent. Math. 81 (1985), 473-514.
    • (1985) Invent. Math. , vol.81 , pp. 473-514
    • Yoshida, T.1
  • 55
    • 0001195414 scopus 로고    scopus 로고
    • Vassiliev invariatnts and a strange identity related to the Dedekind eta-function
    • D. Zagier, Vassiliev invariatnts and a strange identity related to the Dedekind eta-function, Topology 40 (2001), 945-960.
    • (2001) Topology , vol.40 , pp. 945-960
    • Zagier, D.1
  • 56
    • 84895298106 scopus 로고    scopus 로고
    • Physics and Geometry II, eds. P. Cartier, B. Julia, P. Moussa, P. Vanhove, Springer-Verlag, Berlin-Heidelberg-New York
    • D. Zagier, The dilogarithm function, In Frontiers in Number Theory, Physics and Geometry II, eds. P. Cartier, B. Julia, P. Moussa, P. Vanhove, Springer-Verlag, Berlin-Heidelberg-New York, (2006), 3-65.
    • (2006) The dilogarithm function, Frontiers in Number Theory , pp. 3-65
    • Zagier, D.1
  • 57
    • 85039679570 scopus 로고    scopus 로고
    • Algebraic and asymptotic properties of quantum invariants of knots, in preparation
    • D. Zagier, Algebraic and asymptotic properties of quantum invariants of knots, in preparation.
    • Zagier, D.1


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