Near-extremal black holes are usually studied by zooming into the throat that describes their near-horizon geometry. Within this throat, one can argue that two-dimensional JT gravity is the appropriate effective theory that dominates at low temperature. Here, we discuss how to capture this effective description by standing far away from the horizon. Our strategy is to construct a phase space within gravitational theories in AdS that fixes the radial dependence while keeping the transverse dependence arbitrary. This allows us to implement a decoupling limit directly on the phase space while keeping the coordinates fixed. With this, we can relate the effective description in JT gravity to the CFT description at the boundary of AdS , which we do explicitly in AdS and non-rotating configurations in AdS . From the perspective of the dual CFT, our decoupling limit should be understood as a flow between a CFT and a near-CFT . Our analysis shows that local counterterms can be constructed in the near-CFT , which arise from the anomalies (or absence of them) in the CFT . We show that one of these counterterms is the Schwarzian effective action, making this sector a scheme-dependent choice. This illustrates the delicate interplay between a far and a near analysis of near-extremal black holes.

United Kingdom

Alejandra Castro

United States

Robinson Mancilla

Greece

Ioannis Papadimitriou

Near-extremal dynamics away from the horizon

We provide a first principles derivation of the supersymmetric Casimir energy of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SCFTs in four dimensions using the supercharge algebra on general conformal supergravity backgrounds that admit Killing spinors. The superconformal Ward identities imply that there exists a continuous family of conserved R-currents on supersymmetric backgrounds, as well as a continuous family of conserved currents for each conformal Killing vector. These continuous families interpolate between the consistent and covariant R-current and energy-momentum tensor. The resulting Casimir energy, therefore, depends on two continuous parameters corresponding to the choice of conserved currents used to define the energy and R-charge. This ambiguity is in addition to any possible scheme dependence due to local terms in the effective action. As an application, we evaluate the general expression for the supersymmetric Casimir energy we obtain on a family of backgrounds with the cylinder topology ℝ × S 3 and admitting a single Majorana supercharge. Our result is a direct consequence of the supersymmetry algebra, yet it resembles more known expressions for the non-supersymmetric Casimir energy on such backgrounds and differs from the supersymmetric Casimir energy obtained from the zero temperature limit of supersymmetric partition functions. We defer a thorough analysis of the relation between these results to future work.

South Korea

Pantelis Panopoulos

Supersymmetric Casimir energy on   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 conformal supergravity backgrounds

We develop an effective superpotential formalism for the SU(2)×U(1) invariant sector of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauged supergravity in five dimensions with a U(1)3 Fayet-Iliopoulos gauging, and determine the exact superpotential that describes all 1/4 BPS solutions in this sector. This includes the Gutowski-Reall black holes, but also a much broader class of solutions with a squashed S 3, magnetic flux and vector multiplet sources, as well as complex Euclidean BPS saddles. Some of these solutions are known only numerically, but the exact superpotential allows us to analytically evaluate the on-shell action, holographic one-point functions and conserved charges of all BPS solutions and to study their thermodynamics. In particular, by examining the supersymmetry Ward identities we show that solutions with supersymmetric vector multiplet sources break supersymmetry spontaneously. We also demonstrate the first law for black holes in the SU(2)×U(1) invariant sector and show that the conserved charges of supersymmetric solutions satisfy the generalized BPS relation derived in [1], which includes the supersymmetric Casimir energy as a consequence of the anomalous supersymmetry transformation of the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supercurrent at the boundary. Finally, we show that the effective superpotential provides a unifying entropy extremization principle, reproducing Sen’s entropy function for near extremal black holes and the Hosseini-Hristov-Zaffaroni functional for complex Euclidean BPS saddles.

Praxitelis Ntokos

China

Black hole superpotential as a unifying entropy function and BPS thermodynamics

We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons actions in one dimension higher, which are used to supersymmetrize flavor anomalies in <math><mi>d</mi><mo>=</mo><mn>4</mn></math> and, for <math><mi>d</mi><mo>=</mo><mn>2</mn></math> <math><mi>N</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math>, flavor anomalies with <math><mrow><mi>p</mi></mrow></math>, <math><mrow><mi>q</mi><mo>≤</mo><mn>3</mn></mrow></math> and Lorentz-Weyl anomalies with <math><mrow><mi>p</mi></mrow></math>, <math><mrow><mi>q</mi><mo>≤</mo><mn>6</mn></mrow></math>. Finally, we extend the Becchi-Rouet-Stora-Tyutin algebra and the subsequent descent, a necessity for the diffeomorphism anomaly in retrospect. The same modification computes the supersymmetrized anomalies and determines the above Chern-Simons actions when these exist.

France

Ruben Minasian

Piljin Yi

Anomalies and supersymmetry

We provide a non-conformal generalization of the Compère-Song-Strominger (CSS) boundary conditions for AdS3 gravity that breaks the   <math> <mover> <mi>u</mi> <mo>̂</mo> </mover> <mfenced> <mn>1</mn> </mfenced> </math>  $$ \hat{u}(1) $$  Kac-Moody-Virasoro symmetry to two u(1)s. The holographic dual specified by the new boundary conditions can be understood as an irrelevant deformation of a warped conformal field theory (WCFT). Upon consistent reduction to two dimensions, AdS3 gravity results in a deformed Jackiw-Teitelboim dilaton gravity model coupled to a Maxwell field. We show that near extremality the boundary conditions inherited from generalized CSS boundary conditions in three dimensions give rise to an effective action exhibiting the same symmetry breaking pattern as the complex Sachdev-Ye-Kitaev models. Besides the Schwarzian term reflecting the breaking of conformal symmetry, the effective action contains an additional term that captures the breaking of the   <math> <mover> <mi>u</mi> <mo>̂</mo> </mover> <mfenced> <mn>1</mn> </mfenced> </math>  $$ \hat{u}(1) $$  Kac-Moody symmetry.

Pankaj Chaturvedi

Wei Song

Boyang Yu

AdS3 gravity and the complex SYK models

We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-loop computation using a supersymmetric Pauli-Villars regulator.

Georgios Katsianis

Kostas Skenderis

Marika Taylor

Supersymmetry anomaly in the superconformal Wess-Zumino model

We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms.

Chile

Giorgos Anastasiou

Olivera Miskovic

Rodrigo Olea

Counterterms, Kounterterms, and the variational problem in AdS gravity

We determine the general structure of quantum anomalies for the R-multiplet of four dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor multiplets. By solving the Wess-Zumino consistency conditions for off-shell new minimal supergravity in four dimensions with an arbitrary number of Abelian vector multiplets, we compute the anomaly in the conservation of the supercurrent to leading non trivial order in the gravitino and vector multiplet fermions. We find that both R-symmetry and flavor anomalies necessarily lead to a supersymmetry anomaly, thus generalizing our earlier results to non superconformal theories with Abelian flavor symmetries. The anomaly in the conservation of the supercurrent leads to an anomalous transformation for the supercurrent under rigid supersymmetry on bosonic backgrounds that admit new minimal Killing spinors. The resulting deformation of the supersymmetry algebra has implications for supersymmetric localization computations on such backgrounds.

Supersymmetry anomalies in new minimal supergravity

We show that supersymmetry is anomalous in <math><mi>N</mi><mo>=</mo><mn>1</mn></math> superconformal quantum field theories (SCFTs) with an anomalous <math><mi>R</mi></math> symmetry. This anomaly was originally found in holographic SCFTs at strong coupling. Here we show that this anomaly is present, in general, and demonstrate it for the massless superconformal Wess-Zumino model via a one-loop computation. The anomaly appears first in four-point functions of two supercurrents either with two <math><mi>R</mi></math> currents or with an <math><mi>R</mi></math> current and an energy-momentum tensor. In fact, the Wess-Zumino consistency conditions together with the standard <math><mi>R</mi></math>-symmetry anomaly imply the existence of the anomaly. We outline the implications of this anomaly.

Anomalous Supersymmetry

We solve the Wess-Zumino consistency conditions of   <math> <mi>N</mi> <mo>=</mo> <mn>1</mn> </math>  $$ \mathcal{N}=1 $$  off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary a and c anomaly coefficients to leading non trivial order in the gravitino. Besides the well known Weyl and R-symmetry anomalies, we compute explicitly the fermionic   <math> <mi>Q</mi> </math>  $$ \mathcal{Q} $$ - and   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ -supersymmetry anomalies. In particular, we show that   <math> <mi>Q</mi> </math>  $$ \mathcal{Q} $$ -supersymmetry is anomalous if and only if R-symmetry is anomalous. The   <math> <mi>Q</mi> </math>  $$ \mathcal{Q} $$ - and   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ -supersymmetry anomalies give rise to an anomalous supersymmetry transformation for the supercurrent on curved backgrounds admitting Killing spinors, resulting in a deformed rigid supersymmetry algebra. Our results may have implications for supersymmetric localization and supersymmetry phenomenology. Analogous results are expected to hold in dimensions two and six and for other supergravity theories. The present analysis of the Wess-Zumino consistency conditions reproduces the holographic result of  arXiv:1703.0429   and generalizes it to arbitrary a and c anomaly coefficients.