Abstract
When mass-deformed ABJM theory is considered on S 3, the partition function of the theory localises, and is given by a matrix model. At large N, we solve this model in the decompactification limit, where the radius of the three-sphere is taken to infinity. In this limit, the theory exhibits a rich phase structure with an infinite number of third-order quantum phase transitions, accumulating at strong coupling.
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References
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
E. Brézin, C. Itzykson, G. Parisi and J.B. Zuber, Planar Diagrams, Commun. Math. Phys. 59 (1978) 35 [INSPIRE].
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].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [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].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
D. Martelli and J. Sparks, The large N limit of quiver matrix models and Sasaki-Einstein manifolds, Phys. Rev. D 84 (2011) 046008 [arXiv:1102.5289] [INSPIRE].
S. Cheon, H. Kim and N. Kim, Calculating the partition function of N = 2 Gauge theories on S 3 and AdS/CFT correspondence, JHEP 05 (2011) 134 [arXiv:1102.5565] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N = 2 Field Theories on the Three-Sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
H. Fuji, S. Hirano and S. Moriyama, Summing Up All Genus Free Energy of ABJM Matrix Model, JHEP 08 (2011) 001 [arXiv:1106.4631] [INSPIRE].
D.R. Gulotta, C.P. Herzog and S.S. Pufu, Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories, JHEP 11 (2011) 149 [arXiv:1106.5484] [INSPIRE].
L.F. Alday, M. Fluder and J. Sparks, The large-N limit of M2-branes on Lens spaces, JHEP 10 (2012) 057 [arXiv:1204.1280] [INSPIRE].
B. Assel, J. Estes and M. Yamazaki, Large-N Free Energy of 3d N = 4 SCFTs and AdS 4 /CFT 3, JHEP 09 (2012) 074 [arXiv:1206.2920] [INSPIRE].
S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A One-Loop Test of Quantum Supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].
D.Z. Freedman and S.S. Pufu, The holography of F-maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].
D. Farquet and J. Sparks, Wilson loops and the geometry of matrix models in AdS 4 /CFT 3, JHEP 01 (2014) 083 [arXiv:1304.0784] [INSPIRE].
Y. Hatsuda, M. Mariño, S. Moriyama and K. Okuyama, Non-perturbative effects and the refined topological string, arXiv:1306.1734 [INSPIRE].
D. Marmiroli, Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM theory, arXiv:1312.2972 [INSPIRE].
A. Lewkowycz and J. Maldacena, Exact results for the entanglement entropy and the energy radiated by a quark, JHEP 05 (2014) 025 [arXiv:1312.5682] [INSPIRE].
M.S. Bianchi, L. Griguolo, M. Leoni, S. Penati and D. Seminara, BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis, JHEP 06 (2014) 123 [arXiv:1402.4128] [INSPIRE].
N. Gromov and G. Sizov, Exact Slope and Interpolating Functions in ABJM Theory, arXiv:1403.1894 [INSPIRE].
D. Farquet, J. Lorenzen, D. Martelli and J. Sparks, Gravity duals of supersymmetric gauge theories on three-manifolds, arXiv:1404.0268 [INSPIRE].
M. Honda and K. Okuyama, Exact results on ABJ theory and the refined topological string, arXiv:1405.3653 [INSPIRE].
A. Dabholkar, N. Drukker and J. Gomes, Localization in Supergravity and Quantum AdS 4 /CF T 3 Holography, arXiv:1406.0505 [INSPIRE].
A. Barranco and J.G. Russo, Large-N phase transitions in supersymmetric Chern-Simons theory with massive matter, JHEP 03 (2014) 012 [arXiv:1401.3672] [INSPIRE].
J.G. Russo and K. Zarembo, Massive N = 2 Gauge Theories at Large-N, JHEP 11 (2013) 130 [arXiv:1309.1004] [INSPIRE].
J.G. Russo and K. Zarembo, Evidence for Large-N Phase Transitions in N = 2* Theory, JHEP 04 (2013) 065 [arXiv:1302.6968] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
M. Mariño, Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories, J. Phys. A 44 (2011) 463001 [arXiv:1104.0783] [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].
N. Halmagyi and V. Yasnov, The spectral curve of the lens space matrix model, JHEP 11 (2009) 104 [hep-th/0311117] [INSPIRE].
J.G. Russo and K. Zarembo, Localization at large N, arXiv:1312.1214 [INSPIRE].
T. Suyama, On Large-N Solution of ABJM Theory, Nucl. Phys. B 834 (2010) 50 [arXiv:0912.1084] [INSPIRE].
T. Suyama, Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories, Nucl. Phys. B 856 (2012) 497 [arXiv:1106.3147] [INSPIRE].
G. Giasemidis, R.J. Szabo and M. Tierz, Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models, Phys. Rev. D 89 (2014) 025016 [arXiv:1310.3122] [INSPIRE].
F. David, Phases of the large-N matrix model and nonperturbative effects in 2 − D gravity, Nucl. Phys. B 348 (1991) 507 [INSPIRE].
S. Cheon, H.-C. Kim and S. Kim, Holography of mass-deformed M2-branes, arXiv:1101.1101 [INSPIRE].
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Anderson, L., Zarembo, K. Quantum phase transitions in mass-deformed ABJM matrix model. J. High Energ. Phys. 2014, 21 (2014). https://doi.org/10.1007/JHEP09(2014)021
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DOI: https://doi.org/10.1007/JHEP09(2014)021