29 research outputs found
Equivariant localization in supergravity
We show that supersymmetric supergravity solutions with an R-symmetry Killing
vector are equipped with a set of equivariantly closed forms. Various physical
observables may be expressed as integrals of these forms, and then evaluated
using the Berline-Vergne-Atiyah-Bott fixed point theorem. We illustrate with a
variety of holographic examples, including on-shell actions, black hole
entropies, central charges, and scaling dimensions of operators. The resulting
expressions depend only on topological data and the R-symmetry vector, and
hence may be evaluated without solving the supergravity equations.Comment: 6 page
Localizing Wrapped M5-branes and Gravitational Blocks
We consider , SCFTs that can arise from M5-branes
wrapping four-dimensional, complex, toric manifolds and orbifolds. We use
equivariant localization to compute the off-shell central charge of the dual
supergravity solutions, obtaining a result which can be written as a sum of
gravitational blocks and precisely agrees with a field theory computation using
anomaly polynomials and -extremization.Comment: 6 page
The holographic supersymmetric Casimir energy
We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S 1 × M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S 1 ×R 4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating
divergences in observables in asymptotically locally AdS spacetimes. For dual
boundary field theories which are supersymmetric it is natural to ask whether
this defines a supersymmetric renormalization scheme. Recent results in
localization have brought this question into sharp focus: rigid supersymmetry
on a curved boundary requires specific geometric structures, and general
arguments imply that BPS observables, such as the partition function, are
invariant under certain deformations of these structures. One can then ask if
the dual holographic observables are similarly invariant. We study this
question in minimal N = 2 gauged supergravity in four and five dimensions. In
four dimensions we show that holographic renormalization precisely reproduces
the expected field theory results. In five dimensions we find that no choice of
standard holographic counterterms is compatible with supersymmetry, which leads
us to introduce novel finite boundary terms. For a class of solutions
satisfying certain topological assumptions we provide some independent tests of
these new boundary terms, in particular showing that they reproduce the
expected VEVs of conserved charges.Comment: 70 pages; corrected typo
Supercurrent anomalies in 4d SCFTs
We use holographic renormalization of minimal \mathcalN=2 gauged
supergravity in order to derive the general form of the quantum Ward identities
for 3d \mathcalN=2 and 4d \mathcalN=1 superconformal theories on
general curved backgrounds, including an arbitrary fermionic source for the
supercurrent. The Ward identities for 4d \mathcalN=1 theories contain both
bosonic and fermionic global anomalies, which we determine explicitly up to
quadratic order in the supercurrent source. The Ward identities we derive apply
to any superconformal theory, independently of whether it admits a holographic
dual, except for the specific values of the and anomaly coefficients,
which are equal due to our starting point of a two-derivative bulk supergravity
theory. In the case of 4d \mathcalN=1 superconformal theories, we show that
the fermionic anomalies lead to an anomalous transformation of the supercurrent
under rigid supersymmetry on backgrounds admitting Killing spinors, even if all
anomalies are numerically zero on such backgrounds. The anomalous
transformation of the supercurrent under rigid supersymmetry leads to an
obstruction to the -exactness of the stress tensor in supersymmetric vacua,
and may have implications for the applicability of localization techniques. We
use this obstruction to the -exactness of the stress tensor in order to
resolve a number of apparent paradoxes relating to the supersymmetric Casimir
energy, the BPS condition for supsersymmetric vacua, and the compatibility of
holographic renormalization with supersymmetry, that were presented in the
literature
Gravitational free energy in topological AdS/CFT
We define and study a holographic dual to the topological twist of N = 4 gauge theories
on Riemannian three-manifolds. The gravity duals are solutions to four-dimensional
N = 4 gauged supergravity, where the three-manifold arises as a conformal boundary.
Following our previous work, we show that the renormalized gravitational free energy of
such solutions is independent of the boundary three-metric, as required for a topological
theory. We then go further, analyzing the geometry of supersymmetric bulk solutions.
Remarkably, we are able to show that the gravitational free energy of any smooth
four-manifold filling of any three-manifold is always zero. Aided by this analysis, we
prove a similar result for topological AdS5/CFT4. We comment on the implications of
these results for the large N limits of topologically twisted gauge theories in three and
four dimensions, including the ABJM theory and N = 4 SU(N) super-Yang{Mills,
respectively
Gravitational free energy in topological AdS/CFT
We define and study a holographic dual to the topological twist of N = 4 gauge theories on Riemannian three-manifolds. The gravity duals are solutions to four-dimensional N = 4 gauged supergravity, where the three-manifold arises as a conformal boundary. Following our previous work, we show that the renormalized gravitational free energy of such solutions is independent of the boundary three-metric, as required for a topological theory. We then go further, analyzing the geometry of supersymmetric bulk solutions. Remarkably, we are able to show that the gravitational free energy of any smooth four-manifold filling of any three-manifold is always zero. Aided by this analysis, we prove a similar result for topological AdS5/CFT4. We comment on the implications of these results for the large N limits of topologically twisted gauge theories in three and four dimensions, including the ABJM theory and N = 4 SU(N) super-Yang{Mills, respectively
Equivariant localization for AdS/CFT
Abstract We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS 5 × M 6 and AdS 3 × M 8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed