Positive Mass in Scalar-Torsion Holography

TL;DR

This paper explores the holographic renormalization of scalar-torsion gravity with non-minimal derivative coupling, demonstrating how the non-minimal coupling influences the dual scalar operator's properties in an AdS/CFT framework.

Contribution

It introduces a formalism for analyzing scalar-torsion gravity with non-minimal coupling, showing how to obtain non-tachyonic bulk scalars with tunable effective mass.

Findings

The asymptotic solutions lead to AdS geometry for negative cosmological constants.

The non-minimal coupling affects the conformal dimension of the dual operator.

The effective bulk mass can be tuned via the non-minimal coupling.

Abstract

We investigate the holographic renormalization of scalar-torsion gravity in a four-dimensional bulk spacetime with non-minimal derivative coupling. The asymptotic behavior of the static equations leads to an anti-de Sitter geometry for negative cosmological constants, allowing for a holographic interpretation via the AdS/CFT correspondence. The existence of unique solutions throughout the bulk is addressed. We study the effect of the non-minimal coupling parameter on the conformal dimension and the expectation value of the dual scalar operator, showing that the effective bulk mass can be tuned through the non-minimal coupling. Our results provide a formalism for finding non-tachyonic bulk scalar fields which vanish at the boundary.