Abstract
The one-loop partition function of the f(R,R_{mu nu }R^{mu nu }) gravity theory is obtained around hbox {AdS}_4 background. After a 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 the hbox {AdS}_4 space is also computed and the thermal partition function is obtained for this theory. We then consider quantum corrections to the thermodynamical quantities in some special cases.
Highlights
In this paper, we consider the f (R, Rμν Rμν) gravity theory over the anti-de Sitter (AdS) background
Using the heat kernel method, we are able to evaluate the determinants appearing in the partition function and compute the traced heat kernel over the thermal quotient of the AdS4 space [30,31], to obtain the thermal partition function in f (R, Rμν Rμν) theory
We were able to find the one-loop partition function of our theory over the AdS4 background, which is of great interest in other contexts, for instance in the AdS/CFT correspondence
Summary
Where f is an arbitrary function with mass dimension 4. In the case of the Einstein gravity with the Lagrangian L = κ2(R − 2 ), the appropriate choice of the gauge fixing parameters, in the relations (3.4) and (3.5), for which the scalar part of Lgauged becomes diagonal would be α = 0, ρ = − κ2 , γ = 1, 2 and the one-loop partition function (3.31) reduces to. We can recover the result of the one-loop partition function of the conformal gravity theory, first presented in [32] In this case, the Lagrangian takes the form. It can be seen that the appropriate choice of the gauge-fixing parameters in this case can be obtained as α = 0, ρ = 0, γ = 1, and the partition function takes the form. Adding terms containing Rμν Rμν produces a secondary tensor contribution to the partition function
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