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 $D\ge 3$ 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 nonminimal 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.

• Received 10 July 2018

DOI:https://doi.org/10.1103/PhysRevD.98.046013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society