Abstract
We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on S3 retains the form of an Airy function, but now includes a phase that scales as Nk in the large-N limit where k is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.
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F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
F. Benini and P. Milan, Black Holes in 4D \( \mathcal{N} \) = 4 Super-Yang-Mills Field Theory, Phys. Rev. X 10 (2020) 021037 [arXiv:1812.09613] [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].
D.L. Jafferis and A. Tomasiello, A Simple class of N = 3 gauge/gravity duals, JHEP 10 (2008) 101 [arXiv:0808.0864] [INSPIRE].
Y. Imamura and K. Kimura, On the moduli space of elliptic Maxwell-Chern-Simons theories, Prog. Theor. Phys. 120 (2008) 509 [arXiv:0806.3727] [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 S3 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].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
M. Mezei and S.S. Pufu, Three-sphere free energy for classical gauge groups, JHEP 02 (2014) 037 [arXiv:1312.0920] [INSPIRE].
M. Honda and S. Moriyama, Instanton Effects in Orbifold ABJM Theory, JHEP 08 (2014) 091 [arXiv:1404.0676] [INSPIRE].
S. Moriyama and T. Nosaka, Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach, JHEP 11 (2014) 164 [arXiv:1407.4268] [INSPIRE].
B. Assel, N. Drukker and J. Felix, Partition functions of 3d \( \hat{D} \)-quivers and their mirror duals from 1d free fermions, JHEP 08 (2015) 071 [arXiv:1504.07636] [INSPIRE].
S. Moriyama and T. Nosaka, Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas, JHEP 09 (2015) 054 [arXiv:1504.07710] [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].
J.T. Liu and Y. Lu, Subleading corrections to the free energy in a theory with N5/3 scaling, JHEP 10 (2020) 169 [arXiv:1912.04722] [INSPIRE].
J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity, JHEP 01 (2018) 026 [arXiv:1707.04197] [INSPIRE].
J.T. Liu, L.A. Pando Zayas and S. Zhou, Subleading Microstate Counting in the Dual to Massive Type IIA, arXiv:1808.10445 [INSPIRE].
L.A. Pando Zayas and Y. Xin, Topologically twisted index in the ’t Hooft limit and the dual AdS4 black hole entropy, Phys. Rev. D 100 (2019) 126019 [arXiv:1908.01194] [INSPIRE].
M. Hanada, M. Honda, Y. Honma, J. Nishimura, S. Shiba and Y. Yoshida, Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant, JHEP 05 (2012) 121 [arXiv:1202.5300] [INSPIRE].
T. Suyama, A Systematic Study on Matrix Models for Chern-Simons-matter Theories, Nucl. Phys. B 874 (2013) 528 [arXiv:1304.7831] [INSPIRE].
T. Suyama, Linear Chern-Simons-matter Theories in the Planar Limit, JHEP 08 (2019) 083 [arXiv:1904.11728] [INSPIRE].
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ArXiv ePrint: 2008.09642
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Liu, J.T., Zhang, X. The large-N partition function for non-parity-invariant Chern-Simons-matter theories. J. High Energ. Phys. 2020, 7 (2020). https://doi.org/10.1007/JHEP12(2020)007
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DOI: https://doi.org/10.1007/JHEP12(2020)007