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Holographic renormalization and supersymmetry

Research output: Contribution to journalArticle

Pietro Benetti Genolini, Davide Cassani, Dario Martelli, James Sparks

Original languageEnglish
Article number132
Number of pages72
Issue number2
Early online date27 Feb 2017
Accepted/In press18 Feb 2017
E-pub ahead of print27 Feb 2017

Bibliographical note

70 pages; corrected typos


King's Authors


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.

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