Holographic renormalization and supersymmetry

Abstract

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.

70 pages; corrected typos

References in corpus (13)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Localization on Hopf surfaces
• Gauged supergravity from type IIB string theory on Y^{p,q} manifolds
• Holographic renormalization as a canonical transformation
• N=1 and N=2 pure supergravities on a manifold with boundary
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Comments on the Casimir energy in supersymmetric field theories
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Supersymmetric counterterms from new minimal supergravity
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Anti-Self-Dual Solutions
• Tensor calculus for supergravity on a manifold with boundary
• On a class of 4D Kahler bases and AdS_5 supersymmetric Black Holes
• Wilson loops on three-manifolds and their M2-brane duals

Cited by in corpus (9)

• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• AdS${}_5$ Holography and Higher-Derivative Supergravity
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Anomalous Supersymmetry
• The Supersymmetry of Higher-Derivative Supergravity in AdS${}_4$ Holography
• On the uniqueness of supersymmetric AdS${}_5$ black holes with toric symmetry
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere