Trace anomaly and counterterms in designer gravity

  • Andrés Anabalón
  • Dumitru Astefanesei
  • David Choque
  • Cristián Martínez
Open Access
Regular Article - Theoretical Physics

Abstract

We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS4, so that the total action is finite on-shell and satisfy a well defined variational principle. We focus on scalar fields with the conformal mass m 2 = −2l −2 and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar field. In the case of a vanishing anomaly, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of four-dimensional gauged \( \mathcal{N}=8 \) supergravity and its ω-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

Keywords

AdS-CFT Correspondence Black Holes Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Andrés Anabalón
    • 1
  • Dumitru Astefanesei
    • 2
    • 3
  • David Choque
    • 3
    • 4
  • Cristián Martínez
    • 5
  1. 1.Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y CienciasUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaísoChile
  3. 3.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany
  4. 4.Universidad Técnica Federico Santa MaríaValparaísoChile
  5. 5.Centro de Estudios Científicos (CECs)ValdiviaChile

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