Localization in supergravity and quantum AdS 4 /CFT3 holography

We study four-dimensional quantum gravity with negative cosmological constant in the minisuperspace approximation and compute the partition function for the S 3 boundary geometry. In this approximation scheme the path integrals become dominated by a class of asymptotically AdS "microstate geometries." Despite the fact that the theory is pure Einstein gravity without supersymmetry, the result precisely reproduces, up to higher curvature corrections, the Airy function in the S 3 partition function of the maximally supersymmetric Chern-Simons-matter (CSM) theory which sums up all perturbative 1/N corrections. We also show that this can be interpreted as a concrete realization of the idea that the CFT partition function is a solution to the Wheeler-DeWitt equation as advocated in the holographic renormalization group. Furthermore, the agreement persists upon the inclusion of a string probe and it reproduces the Airy function in the vev of half-BPS Wilson loops in the CSM theory. These results may suggest that the supergravity path integrals localize to the minisuperspace in certain cases and the use of the minisuperspace approximation in AdS/CFT may be a viable approach to study 1/N corrections to large N CFTs.

Section: Jhep06(2018)106mentioning

confidence: 93%

Section: The S Partition Functionmentioning

confidence: 95%

See 1 more Smart Citation

Airy function and 4d quantum gravity

Caputa

Hirano

2018

“…The projection condition (4.7) then implies 45) which are equivalent to (3.10). The projection condition (4.7) also constrains the number of fermionic operators in a way similar to (3.12).…”

Section: Usp(2n ) Internal Symmetrymentioning

confidence: 99%

ABJ quadrality

Honda

Pang

Zhu

2017

Abstract:We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d N = 6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS 4 × CP 3 and N = 6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS 4 . After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N 1 ) × USp(2N 2 ) while the background of the string theory is replaced by AdS 4 × CP 3 /Z 2 , and the supersymmetries in the both theories reduce to N = 5. We propose that adding the orientifolds to the N = 6 Vasiliev theory leads to N = 5 SUSY Vasiliev theory. It turns out that the N = 5 case is more involved because there are two formulations of the N = 5 Vasiliev theory with either O or USp internal symmetry. We show that the two N = 5 Vasiliev theories can be understood as certain projections of the N = 6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N 1 ) × USp(2N 2 ) ABJ theory has the two vector model like limits: N 2 ≫ N 1 and N 1 ≫ N 2 which correspond to the semi-classical N = 5 Vasiliev theories with O(N 1 ) and USp(2N 2 ) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the N = 5 ABJ theory, string/M-theory and two N = 5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the N = 5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the N = 6 Vasiliev theory and the parameters in the N = 6 ABJ theory, which was conjectured in [1].

“…Along the line of the interpretation in the gravity dual, it is very interesting to note that the coefficient of the one-loop log term was studied from the gravity side [67] and the match with the expansion of the Airy function (1.1) was found. Also, very recently, the Airy function was reproduced from the localization computation in the gauged supergravity [68]. Finally, though we have used the matrix model (2.2) obtained after localization for the partition functions of superconformal Chern-Simons theories, it would be interesting to study the non-perturbative instanton effects directly from the field-theoretical viewpoints.…”

Section: Jhep11(2014)164mentioning

confidence: 99%

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

Moriyama

Nosaka

2014

Abstract:We study the partition function of three-dimensional N = 4 superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as Z(N ) = e A C −1/3 Ai[C −1/3 (N − B)] with coefficients C, B and A and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of B for general N = 4 theories, a conjectural form of A for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.