On Entropy Function for Supersymmetric Black Rings

TL;DR

This paper calculates the entropy function for five-dimensional supersymmetric black rings using on-shell and off-shell formalisms, including higher order corrections, and compares the results with microscopic calculations.

Contribution

It provides a detailed computation of the entropy function for supersymmetric black rings, incorporating higher order corrections and comparing with microscopic results.

Findings

Entropy function reproduces Bekenstein-Hawking entropy at tree level.

Higher order corrections from Gauss-Bonnet and R^2 terms are computed.

Results are consistent with previous microscopic calculations.

Abstract

The entropy function for five-dimensional supersymmetric black rings, which are solutions of $U(1)^{3}$ minimal supergravity, is calculated via both on-shell and off-shell formalism. We find that at the tree level, the entropy function obtained from both perspectives can reproduce the Bekenstein-Hawking entropy. We also compute the higher order corrections to the entropy arising form five-dimensional Gauss-Bonnet term as well as supersymmetric $R^{2}$ completion respectively and compare the results with previous microscopic calculations.