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Trace Anomaly and Counterterms in Designer Gravity

Anabalon, A., Astefanesei, D., Choque, D., & Martinez, C. (2016). Trace Anomaly and Counterterms in Designer Gravity. Journal of high energy physics: JHEP, 2016(03): 117. doi:10.1007/JHEP03(2016)117.

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Genre: Journal Article
Other : Conformal Anomaly and Counterterms in Designer Gravity (Former title)

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### Creators

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Creators:
Anabalon, Andres, Author
Astefanesei, Dumitru1, Author
Choque, David1, Author
Martinez, Cristian, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract: We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS$_{4}$, so that the total action is finite on-shell and satisfy a well defined variational principle for an arbitrary scalar field potential. 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 conformal 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 conformal 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. When the anomaly vanishes, 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 $\omega$-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

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Dates: 2015-11-272016
Publication Status: Published in print
Pages: 26 pages, no figures
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1511.08759
URI: http://arxiv.org/abs/1511.08759
DOI: 10.1007/JHEP03(2016)117
Degree: -

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### Source 1

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Title: Journal of high energy physics : JHEP
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2016 (03) Sequence Number: 117 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: /journals/resource/111021927548002