Entropy Functions with 5D Chern-Simons terms

TL;DR

This paper extends Sen's entropy function analysis to five-dimensional supergravity with Chern-Simons terms, demonstrating gauge invariance and correct charge identification directly in 5D, and clarifying the relation between black hole and black ring geometries.

Contribution

It provides a systematic 5D approach to entropy functions with Chern-Simons terms, fixing charge mismatches and interpreting geometric transitions.

Findings

Entropy function remains gauge invariant in 5D.

Electric charges are identified as Page charges.

The e^0 - p^0 exchange interpolates between black hole and black ring geometries.

Abstract

In this note we reconsider Sen's entropy function analysis for 5D supergravity actions containing Chern-Simons terms. The apparent lack of gauge invariance is usually tackled via a 4D reduction. Here we motivate how a systematic 5D procedure also works. In doing so, it becomes important to identify the correct 5D charges. In particular, we perform explicit calculations for the black ring and 5D black hole. In the black ring analysis, we find Chern-Simons induced spectral flow shifts emerging out of Sen's formalism. We find that the entropy function nevertheless remains gauge invariant and the resulting electric charges are identified as Page charges. For the black hole too, 5D gauge invariance is confirmed. Our 5D analysis enables us to fix a mismatch that arose in the electric charges of Goldstein and Jena's 4D-reduced calculation. Finally we provide an interpretation for the e^0 - p^0 exchange in the entropy function as an interpolation between black hole and black ring geometries in Taub-NUT.