Holographic c-theorem and Born-Infeld Gravity Theories

TL;DR

This paper demonstrates that certain Born-Infeld gravity theories in higher dimensions admit a holographic c-function, providing a new class of higher derivative models with this property, including a specific non-minimal extension of new massive gravity.

Contribution

It shows that fixed-parameter Born-Infeld gravity theories can possess a holographic c-function, expanding the class of higher derivative theories with this property.

Findings

Born-Infeld theories admit a holographic c-function when parameters are fixed.

The D=3 non-minimal Born-Infeld extension of new massive gravity is explicitly constructed.

An infinite series of higher derivative models with a c-function are generated.

Abstract

The requirement of the existence of a holographic c-function for higher derivative theories is a very restrictive one and hence most theories do not possess this property. Here, we show that, when some of the parameters are fixed, the $D\geq3$ Born-Infeld gravity theories admit a holographic c-function. We work out the details of the $D=3$ theory with no free parameters, which is a non-minimal Born-Infeld type extension of new massive gravity. Moreover, we show that these theories generate an infinite number of higher derivative models admitting a c-function in a suitable expansion and therefore they can be studied at any truncated order.