TY - JOUR

T1 - Trace anomaly and counterterms in designer gravity

AU - Anabalón, Andrés

AU - Astefanesei, Dumitru

AU - Choque, David

AU - Martínez, Cristián

N1 - Funding Information:
DA would like to thank Stefan Theisen for interesting discussions on conformal anomalies. DA and DC acknowledge the hospitality of the Albert Einstein Institute in Potsdam during the last stages of this research. This work has been done with partial support from the Fondecyt grants 11121187, 1120446, 1121031,1130658, and 1141073 and by the Newton-Picarte Grants DPI20140053 and DPI20140115. D. C. thanks CONICYT for a Ph.D. scholarship. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of Conicyt.
Publisher Copyright:
© 2016, The Author(s).

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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 m2 = −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 (Formula presented.) supergravity and its ω-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

AB - 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 m2 = −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 (Formula presented.) supergravity and its ω-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

KW - AdS-CFT Correspondence

KW - Black Holes

KW - Gauge-gravity correspondence

UR - http://www.scopus.com/inward/record.url?scp=84962581752&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2016)117

DO - 10.1007/JHEP03(2016)117

M3 - Article

AN - SCOPUS:84962581752

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 117

ER -