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

TL;DR

The work analyzes the Born-Infeld extension of New Massive Gravity in three dimensions, deriving its equations of motion and examining constant-curvature and asymptotically AdS spaces. By enforcing the null-energy condition and holographic principles, it identifies two simple c-functions, one of which reproduces the Einstein gravity c-function, with the boundary value yielding the Virasoro central charge and Weyl anomaly up to a constant. At fixed points, the c-function coincides with the central charge, while holographic renormalization confirms the Weyl anomaly coefficient, and BI-NMG avoids vacuum degeneracy present in standard NMG. These results tie BI-NMG to AdS3/CFT2 and holographic c-theorems, offering a consistent, higher-order gravity framework with well-defined boundary data, albeit with open questions about bulk and boundary unitarity.

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.