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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.
