Holographic c -theorem and Born-Infeld gravity theories

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 ≥ 3 Born-Infeld gravity theories admit a holographic c-function. We work out the details of the D ¼ 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.

Holographic (a,c) charges and their universal relation in d=6 from massless higher-order gravities

“…In [36,53], this step was circumvented by introducing a free massless scalar. This method was also adopted in [54] to establish the c-theorem in Born-Infeld gravity theories.…”

Instability of BTZ black holes in parity-even massive gravity

“…where G µν = R µν − 1 2 Rg µν is the Einstein tensor, m 2 is a positive definite dimension-full parameter, σ = ±1 is a sign coefficient, λ is a parameter related to the cosmological constant and κ 3 is related to the three dimensional Newton constant as κ 2 3 = 16πG 3 . Note that λ = 0 is excluded from the parameter space since at this point the field redefinition g µν → g µν − σ m 2 G µν makes the theory trivial [16]. Expanding this action in terms of 1/m 2 , which is practically a derivative expansion, has the following interesting feature…”

The holographic c-theorem and infinite-dimensional Lie algebras

“…One criterion is to require the absence of a scalar ghost degree of freedom that arises for an arbitrary choice of the relative coefficients of the higher-derivative terms [10]. From a holographic perspective, demanding the existence of a holographic c-function is another way to single out particular combinations [11][12][13][14].…”