Entropy of Pairs of Dual Attractors in 6D/7D

TL;DR

This paper investigates the entropy and attractor mechanisms of dual pairs of black branes in six and seven-dimensional N=2 supergravity, analyzing moduli space contributions and deriving attractor equations for these systems.

Contribution

It introduces a detailed analysis of the entropy and attractor equations for dual black brane pairs in 6D and 7D supergravity, emphasizing the role of the SO(1,1) moduli space factor.

Findings

Critical dilaton values at the horizon are determined.

Attractor equations for dual black brane pairs are derived.

The influence of the SO(1,1) moduli space factor is clarified.

Abstract

We study the attractor mechanism of dual pairs of black brane bounds in N=2 supergravity in six and seven dimensions. First, we consider the effective potentials of the 6D and 7D black branes as well as their entropies. The contribution coming from the SO(1,1) factor of the moduli spaces M_{6D} and M_{7D} of these theories is carefully analyzed and it is used to motivate the study of the dual black branes bounds; which in turn allow to fix the critical value of the dilaton at horizon. The attractor eqs of the black branes and the bound pairs are derived by combining the criticality conditions of the corresponding effective potentials and the Lagrange multiplier method capturing constraints eqs on the fields moduli.