c-functions in the Born-Infeld extended New Massive Gravity

TL;DR

This paper derives equations for a Born-Infeld extension of New Massive Gravity, explores c-functions related to holography and energy conditions, and connects them to central charges and anomalies in conformal field theories.

Contribution

It introduces and analyzes a Born-Infeld extension of New Massive Gravity, establishing c-functions consistent with holography and energy conditions, and relating them to conformal field theory data.

Findings

Two simple c-functions derived, one matches Einstein gravity's c-function.

At fixed points, c-function yields the Virasoro central charge.

C-functions relate to Weyl anomaly coefficients.

Abstract

We derive and study the equations of motion of the Born-Infeld extension of New Massive Gravity for globally and asymptotically (anti-)de Sitter spaces, and show that the assumptions of the null-energy condition and holography (that bounds the c-function) lead to two simple c-functions one of which is equivalent to the c-function of Einstein's gravity. We also show that, at the fixed point, the c-function gives the central charge of the Virasoro algebra and the coefficient of the Weyl anomaly up to a constant.