Abstract
The partition functions of free bosons as well as fermions on AdS2 are not smooth as a function of their masses. For free bosons, the partition function on AdS2 is not smooth when the mass saturates the Breitenlohner-Freedman bound. We show that the expectation value of the scalar bilinear on AdS2 exhibits a kink at the BF bound and the change in slope of the expectation value with respect to the mass is proportional to the inverse radius of AdS2. For free fermions, when the mass vanishes the partition function exhibits a kink. We show that expectation value of the fermion bilinear is discontinuous and the jump in the expectation value is proportional to the inverse radius of AdS2. We then show the supersymmetric actions of the chiral multiplet on AdS2 × S1 and the hypermultiplet on AdS2 × S2 demonstrate these features. The supersymmetric backgrounds are such that as the ratio of the radius of AdS2 to S1 or S2 is dialled, the partition functions as well as expectation of bilinears are not smooth for each Kaluza-Klein mode on S1 or S2. Our observation is relevant for evaluating one-loop partition function in the near horizon geometry of extremal black holes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Sen, Quantum entropy function from AdS2/CFT1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [INSPIRE].
R.B. Mann and S.N. Solodukhin, Universality of quantum entropy for extreme black holes, Nucl. Phys. B 523 (1998) 293 [hep-th/9709064] [INSPIRE].
S. Banerjee, R.K. Gupta and A. Sen, Logarithmic corrections to extremal black hole entropy from quantum entropy function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].
S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic corrections to N = 4 and N = 8 black hole entropy: a one loop test of quantum gravity, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].
A. Sen, Logarithmic corrections to N = 2 black hole entropy: an infrared window into the microstates, Gen. Rel. Grav. 44 (2012) 1207 [arXiv:1108.3842] [INSPIRE].
A. Sen, Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions, Gen. Rel. Grav. 44 (2012) 1947 [arXiv:1109.3706] [INSPIRE].
C. Keeler, F. Larsen and P. Lisbao, Logarithmic corrections to N ≥ 2 black hole entropy, Phys. Rev. D 90 (2014) 043011 [arXiv:1404.1379] [INSPIRE].
N. Banerjee et al., Supersymmetry, localization and quantum entropy function, JHEP 02 (2010) 091 [arXiv:0905.2686] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP 06 (2011) 019 [arXiv:1012.0265] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Localization & exact holography, JHEP 04 (2013) 062 [arXiv:1111.1161] [INSPIRE].
J.R. David, E. Gava, R.K. Gupta and K. Narain, Boundary conditions and localization on AdS. Part I, JHEP 09 (2018) 063 [arXiv:1802.00427] [INSPIRE].
J.R. David, E. Gava, R.K. Gupta and K. Narain, Boundary conditions and localization on AdS. Part II. General analysis, JHEP 02 (2020) 139 [arXiv:1906.02722] [INSPIRE].
A. Sen, Revisiting localization for BPS black hole entropy, arXiv:2302.13490 [INSPIRE].
A. Pittelli, Supersymmetric localization of refined chiral multiplets on topologically twisted H2 × S1, Phys. Lett. B 801 (2020) 135154 [arXiv:1812.11151] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
A.J. Amsel and D. Marolf, Supersymmetric multi-trace boundary conditions in AdS, Class. Quant. Grav. 26 (2009) 025010 [arXiv:0808.2184] [INSPIRE].
O.J.C. Dias, R. Masachs, O. Papadoulaki and P. Rodgers, Hunting for fermionic instabilities in charged AdS black holes, JHEP 04 (2020) 196 [arXiv:1910.04181] [INSPIRE].
J.R. David, E. Gava, R.K. Gupta and K. Narain, Localization on AdS2 × S1, JHEP 03 (2017) 050 [arXiv:1609.07443] [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Renyi entropies for free field theories, JHEP 04 (2012) 074 [arXiv:1111.6290] [INSPIRE].
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001): strings, branes and extra dimensions, (2002), p. 3 [hep-th/0201253] [INSPIRE].
W. Mueck, Spinor parallel propagator and Green’s function in maximally symmetric spaces, J. Phys. A 33 (2000) 3021 [hep-th/9912059] [INSPIRE].
J.L. Synge, Relativity: the general theory, (1960) [INSPIRE].
P.C. Peters, Covariant electromagnetic potentials and fields in Friedmann universes, J. Math. Phys. 10 (1969) 1216.
B. Allen and T. Jacobson, Vector two point functions in maximally symmetric spaces, Commun. Math. Phys. 103 (1986) 669 [INSPIRE].
N. Hama and K. Hosomichi, Seiberg-Witten theories on ellipsoids, JHEP 09 (2012) 033 [Addendum ibid. 10 (2012) 051] [arXiv:1206.6359] [INSPIRE].
A. Zaffaroni, AdS black holes, holography and localization, Living Rev. Rel. 23 (2020) 2 [arXiv:1902.07176] [INSPIRE].
D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2303.14354
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
David, J.R., Gava, E., Gupta, R.K. et al. Discontinuities of free theories on AdS2. J. High Energ. Phys. 2023, 171 (2023). https://doi.org/10.1007/JHEP09(2023)171
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2023)171