Modified gravity one-loop partition function

TL;DR

This paper computes the one-loop partition function for a modified gravity theory around AdS4, including quantum corrections to thermodynamics, using heat kernel techniques and gauge fixing.

Contribution

It provides the first detailed calculation of the one-loop partition function for $f(R,R_{ u u})$ gravity on AdS4, including thermal effects and quantum corrections.

Findings

Derived the one-loop partition function for the theory.

Computed the heat kernel on AdS4 and its thermal quotient.

Analyzed quantum corrections to thermodynamical quantities.

Abstract

The one-loop partition function of the $f(R,R_{\mu\nu}R^{\mu\nu})$ gravity theory is obtained around AdS$_4$ background. After suitable choice of the gauge condition and computation of the ghost determinant, we obtain the one-loop partition function of the theory. The traced heat kernel over the thermal quotient of AdS$_4$ space is also computed and the thermal partition function is obtained for this theory. We have then consider quantum corrections to the thermodynamical quantities in some special cases.