Euclidean Methods and the entropy function

TL;DR

This paper establishes a connection between Sen's entropy functional formalism and the Euclidean formalism at zero temperature, showing their equivalence and implications for dual CFT thermodynamics.

Contribution

It demonstrates that Sen's entropy function matches the zero-temperature limit of the Euclidean action and aligns with chemical potentials from the Euclidean formalism.

Findings

Sen's entropy function equals the zero-temperature Euclidean action

Near horizon fields in Sen's formalism match Euclidean chemical potentials

Brief discussion on implications for dual CFT thermodynamics

Abstract

We review results of articles hep-th/0607056, hep-th/0610163 and 0704.1405 [hep-th]. Here we focus on establish the connection between the entropy functional formalism of Sen and the standard Euclidean formalism taken at zero temperature. We find that Sen's entropy function $f$ (on-shell) matches the zero temperature limit of the Euclidean action. Moreover, Sen's near horizon angular and electric fields agree with the chemical potentials that are defined from the zero-temperature limit of the Euclidean formalism. Connection with the Dual CFT thermodynamics is briefly discussed.