We present a detailed study of the regularized on-shell action of the recently found asymptotically AdS black hole supergravity solution with three angular momenta and two electric charges. We show that a particular choice of finite counterterms in the holographic renormalization procedure yields a result for the on-shell action of the supersymmetric limit of the black hole solution which is in perfect agreement with the large $\textit{N}$ limit of the superconformal index of the dual 6d 𝒩 = (2, 0) $\textit{A}$ SCFT on $\textit{S}$ × $\textit{S}$ . We also discuss a generalization of this 7d supergravity background to a new general family of black holes with horizons given by the $\textit{L}$ 5d Sasaki-Einstein manifolds. The regularized on-shell action of these new 7d black holes is also in agreement with supersymmetric localization results for the 6d 𝒩 = (2, 0) SCFT on $\textit{S}$ × $\textit{L}$ . Finally, we briefly discuss a generalization of known AdS gauged supergravity backgrounds to new 5d black holes with $\textit{L}$($\textit{p}$, $\textit{q}$) lens space horizon topologies.

Belgium

Nikolay Bobev

Marina David

Italy

Vasil Dimitrov

South Korea

Junho Hong

We use the AdS/CFT correspondence to explicitly calculate some of the three-point functions in the planar limit of the 4d $$ \mathcal{N} $$ = 1 Leigh-Strassler SCFT. This strongly interacting CFT can be obtained as a mass deformation of the 4d $$ \mathcal{N} $$ = 4 SYM theory and admits a dual description in terms of an AdS background of type IIB supergravity. Our analysis is based on the existence of a consistent truncation of the 10d supergravity to a tractable 5d gravitational theory with 10 scalar fields dual to some of the low-lying operators in the spectrum of the LS SCFT. We apply standard holographic techniques to this 10-scalar model to analytically calculate the correlators of interest and thus provide a rare example of explicit three-point functions of scalar non-BPS operators in strongly coupled 4d CFTs. Using superconformal Ward identities we perform several consistency checks of these holographic correlators. As a byproduct of our analysis we discuss some subtleties related to the calculation of extremal correlators in AdS/CFT and the contribution of scalar derivative couplings to the evaluation of Witten diagrams. Our work provides a blueprint for the holographic calculation of other correlators in the LS SCFT and similar top-down holographic models.

Hynek Paul

Holographic correlators beyond maximal supersymmetry

We use holography to study correlation functions of local operators in maximally supersymmetric Yang-Mills theories arising on the world-volume of D$\textit{p}$-branes in the large-$\textit{N}$ and strong-coupling limit. The relevant supergravity backgrounds obtained from the near-horizon limit of the D$\textit{p}$-branes enjoy a scaling similarity, which leads to an auxiliary AdS space of fractional dimension. This suggests that holographic correlation functions in this setup can be computed by integrating standard CFT correlators over the auxiliary extra dimensions. We apply this prescription to analytically compute two- and three-point correlators of scalar operators. The resulting two-point functions take a familiar CFT form but with shifted conformal dimensions, while the three-point correlators have a much more involved position dependence which we calculate explicitly in terms of a sum of Appell functions.

Guillermo Mera Álvarez

Correlation functions for non-conformal D$\textit{p}$-brane holography

We study the sphere partition function of 3d $$ \mathcal{N} $$ = 2 holographic SCFTs arising on the worldvolume of $\textit{N}$ coincident M2-branes in the presence of squashing and real mass deformations. We argue that the all-order large $\textit{N}$ perturbative expansion of the partition function resums into a compact expression in terms of an Airy function. We provide ample evidence for this conjecture using numerical methods, saddle point analysis in the ’t Hooft limit, and the relation of the squashed sphere partition function to the Cardy-like limit of the superconformal index. We also discuss the relation of our results to topological string theory and the statistical mechanics of Fermi gases. Our conjecture has a bearing on the AdS/CFT correspondence and the structure of perturbative M-theory corrections to 11d supergravity which we discuss.

Pieter-Jan Smet

France

Valentin Reys

China

Xuao Zhang

An Airy tale at large $\textit{N}$

We study the maximally supersymmetric Yang-Mills theory on $\textit{S}$ using supersymmetric localisation and holography. We argue that the analytic continuation in dimension to $\textit{d}$ = 1 yields a Euclidean version of the BMN matrix quantum mechanics. This system can be analysed at large $\textit{N}$ using supersymmetric localisation and leads to explicit results for the free energy on $\textit{S}$ and the expectation value of supersymmetric Wilson loops. We show how these results can be reproduced at strong gauge coupling using holography by employing spherical D-brane solutions. We construct these solutions for any value of $\textit{d}$ using an effective supergravity description and pay particular attention to the subtleties arising in the $\textit{d}$ → 1 limit. Our results have implications for the BMN matrix quantum mechanics and the physics of circular D0-branes.

United States

United Kingdom

Pieter Bomans

Iceland

Friðrik Gautason

Spherical branes and the BMN matrix quantum mechanics

We study the superconformal index of 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories on S 1 × ω  S 2 in the Cardy-like limit where the radius of the S 1 is much smaller than that of the S 2. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 holographic superconformal field theories describing the low-energy dynamics of N M2-branes and derive closed form expressions, valid to all orders in the 1/N expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS4 and the four-derivative corrections to 4d gauged supergravity.

Sunjin Choi

Superconformal indices of 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs and holography

We study the logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS4. Our results also have important implications for effective field theory coupled to gravity in AdS4 and for the existence of scale-separated AdS4 vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.

A compendium of logarithmic corrections in AdS/CFT

We continue the holographic exploration of the conformal manifold of 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 S-fold SCFTs constructed by gauging the flavor symmetry of the Gaiotto-Witten T[U(N)] theory. We show how to uplift the two-parameter family of AdS4 vacua dual to this conformal manifold to 10d backgrounds of type IIB supergravity. We use these uplifted solutions to shed new light on the mysterious nature of the infinite distance limit on the conformal manifold and to study probe strings and D3-branes. This analysis uncovers an intriguing structure of the S 3 partition function of the S-fold SCFTs which resembles the giant graviton expansion of the superconformal index of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM. We also show how to each member of the family of supersymmetric AdS4 vacua one can associate a consistent truncation to 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauged supergravity and use this result, in conjunction with holography, to calculate the large N partition function of the 3d S-fold SCFT on compact Euclidean manifolds. Finally, we generalize the supersymmetric AdS4 vacua to a four-parameter family of non-supersymmetric AdS4 solutions.

Jesse Muiden

The conformal manifold of S-folds in string theory

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal SU(N) YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so called E theory is closely related to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM and has a holographic description in terms of a ℤ2 orientifold of AdS5 × S 5. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the ’t Hooft coupling λ. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to sixth order in the λ  −1/2 strong coupling expansion. These results provide explicit field theory predictions for the α′ corrections to the supergravity approximation of type IIB string theory on the AdS5 × S 5 /ℤ2 orientifold.

The planar limit of the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 E-theory: numerical calculations and the large λ expansion

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 holographic SCFTs arising on the worldvolume of N M2-branes. We obtain results for the thermal free energy density on S 1 × ℝ 2, the Casimir energy on T 2 × ℝ, and the three leading coefficients in the large temperature limit of the free energy on S 1 × S 2 valid to subleading order in the large N limit. As a byproduct of our holographic analysis we also present a conjecture for the structure of the large temperature expansion of the thermal free energy of general 3d CFTs on S 1 × S 2.