Abstract
Using the matrix model which calculates the exact free energy of ABJM theory on \( {\mathbb{S}^3} \) we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4 × \( \mathbb{C}{\mathbb{P}^3} \). We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the ’t Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping \( \mathbb{R}{\mathbb{P}^3} \).
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References
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
M. Mariño, Chern-Simons theory, matrix integrals and perturbative three manifold invariants, Commun. Math. Phys. 253 (2004) 25 [hep-th/0207096] [INSPIRE].
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, Matrix model as a mirror of Chern-Simons theory, JHEP 02 (2004) 010 [hep-th/0211098] [INSPIRE].
M. Mariño and P. Putrov, Exact results in ABJM theory from topological strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].
N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].
N. Halmagyi and V. Yasnov, The spectral curve of the lens space matrix model, JHEP 11 (2009) 104 [hep-th/0311117] [INSPIRE].
B. Haghighat, A. Klemm and M. Rauch, Integrability of the holomorphic anomaly equations, JHEP 10 (2008) 097 [arXiv:0809.1674] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
S.H. Shenker, The strength of nonperturbative effects in string theory, in Random surfaces and quantum gravity, O. Álvarez, E. Marinari and P. Windey eds., Plenum, New York U.S.A. (1991) 191.
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041 [hep-th/9407031] [INSPIRE].
E.J. Martinec, The annular report on noncritical string theory, hep-th/0305148 [INSPIRE].
S.Y. Alexandrov, V.A. Kazakov and D. Kutasov, Nonperturbative effects in matrix models and D-branes, JHEP 09 (2003) 057 [hep-th/0306177] [INSPIRE].
E. Brézin, J.-C. Le Guillou and J. Zinn-Justin, Perturbation theory at large order. 2. Role of the vacuum instability, Phys. Rev. D 15 (1977) 1558 [INSPIRE].
M. Mariño, R. Schiappa and M. Weiss, Nonperturbative effects and the large-order behavior of matrix models and topological strings, arXiv:0711.1954 [INSPIRE].
M. Mariño, R. Schiappa and M. Weiss, Multi-Instantons and multi-cuts, J. Math. Phys. 50 (2009) 052301 [arXiv:0809.2619] [INSPIRE].
A. Klemm, M. Mariño and M. Rauch, Direct integration and non-perturbative effects in matrix models, JHEP 10 (2010) 004 [arXiv:1002.3846] [INSPIRE].
O. Bergman and S. Hirano, Anomalous radius shift in AdS 4 /CFT 3, JHEP 07 (2009) 016 [arXiv:0902.1743] [INSPIRE].
O. Aharony, A. Hashimoto, S. Hirano and P. Ouyang, D-brane charges in gravitational duals of 2+1 dimensional gauge theories and duality cascades, JHEP 01 (2010) 072 [arXiv:0906.2390] [INSPIRE].
K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
J.T. Liu and R. Minasian, Computing 1/N 2 corrections in AdS/CFT, arXiv:1010.6074 [INSPIRE].
W. Taylor, M(atrix) theory: matrix quantum mechanics as a fundamental theory, Rev. Mod. Phys. 73 (2001) 419 [hep-th/0101126] [INSPIRE].
F. David, Phases of the large-N matrix model and nonperturbative effects in 2-D gravity, Nucl. Phys. B 348 (1991) 507 [INSPIRE].
F. David, Nonperturbative effects in matrix models and vacua of two-dimensional gravity, Phys. Lett. B 302 (1993) 403 [hep-th/9212106] [INSPIRE].
N. Seiberg and D. Shih, Branes, rings and matrix models in minimal (super)string theory, JHEP 02 (2004) 021 [hep-th/0312170] [INSPIRE].
V.A. Kazakov and I.K. Kostov, Instantons in noncritical strings from the two matrix model, hep-th/0403152 [INSPIRE].
J.C. Le Guillou and J. Zinn-Justin, Large order behavior of perturbation theory, North Holland, Amsterdam The Netherlands (1990).
S. Pasquetti and R. Schiappa, Borel and Stokes nonperturbative phenomena in topological string theory and c = 1 matrix models, Annales Henri Poincaré 11 (2010) 351 [arXiv:0907.4082] [INSPIRE].
M. Aganagic, V. Bouchard and A. Klemm, Topological strings and (almost) modular forms, Commun. Math. Phys. 277 (2008) 771 [hep-th/0607100] [INSPIRE].
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) 485–486] [hep-th/9407087] [INSPIRE].
S. Garoufalidis, A. Its, A. Kapaev and M. Mariño, Asymptotics of the instantons of Painlevé I, arXiv:1002.3634 [INSPIRE].
S. Hikami and E. Brézin, Large order behavior of the 1/n expansion in zero-dimensions and one-dimensions, J. Phys. A 12 (1979) 759 [INSPIRE].
B. Eynard and J. Zinn-Justin, Large order behavior of 2-D gravity coupled to D < 1 matter, Phys. Lett. B 302 (1993) 396 [hep-th/9301004] [INSPIRE].
M. Mariño, Nonperturbative effects and nonperturbative definitions in matrix models and topological strings, JHEP 12 (2008) 114 [arXiv:0805.3033] [INSPIRE].
I.R. Klebanov, String theory in two-dimensions, hep-th/9108019 [INSPIRE].
D. Ghoshal and C. Vafa, C = 1 string as the topological theory of the conifold, Nucl. Phys. B 453 (1995) 121 [hep-th/9506122] [INSPIRE].
A. Polyakov, de Sitter space and eternity, Nucl. Phys. B 797 (2008) 199 [arXiv:0709.2899] [INSPIRE].
A. Polyakov, Global warming of De Sitter space, talk presented at Strings, (2008).
S. Hohenegger and I. Kirsch, A note on the holography of Chern-Simons matter theories with flavour, JHEP 04 (2009) 129 [arXiv:0903.1730] [INSPIRE].
Y. Hikida, W. Li and T. Takayanagi, ABJM with flavors and FQHE, JHEP 07 (2009) 065 [arXiv:0903.2194] [INSPIRE].
P. Koerber and L. Martucci, From ten to four and back again: how to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].
P. Koerber, Lectures on generalized complex geometry for physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
M. Cvetič, H. Lü and C. Pope, Consistent warped space Kaluza-Klein reductions, half maximal gauged supergravities and CP n constructions, Nucl. Phys. B 597 (2001) 172 [hep-th/0007109] [INSPIRE].
T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
T. Nishioka and T. Takayanagi, Fuzzy ring from M2-brane giant torus, JHEP 10 (2008) 082 [arXiv:0808.2691] [INSPIRE].
M.C. Cheng, R. Dijkgraaf and C. Vafa, Non-perturbative topological strings and conformal blocks, JHEP 09 (2011) 022 [arXiv:1010.4573] [INSPIRE].
M. Mariño, S. Pasquetti and P. Putrov, Large-N duality beyond the genus expansion, JHEP 07 (2010) 074 [arXiv:0911.4692] [INSPIRE].
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ArXiv ePrint: 1103.4844
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Drukker, N., Mariño, M. & Putrov, P. Nonperturbative aspects of ABJM theory. J. High Energ. Phys. 2011, 141 (2011). https://doi.org/10.1007/JHEP11(2011)141
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DOI: https://doi.org/10.1007/JHEP11(2011)141