Nernst branes in gauged supergravity

TL;DR

This work extends the first-order flow formalism to static black branes in four-dimensional $N=2$ gauged supergravity with vector multiplets, enabling systematic construction of extremal solutions including Nernst branes with vanishing entropy density. By reformulating flows in big moduli space and exploiting symmetries of charges and fluxes, the authors generate both supersymmetric and non-supersymmetric solutions across several prepotentials, notably including the STU model. They derive exact constant-$\gamma$ solutions and interpolating configurations between $AdS_4$ and $AdS_2 \times \mathbb{R}^2$, as well as non-constant $\gamma$ flows, revealing a rich landscape of extremal geometries and attractor-like behavior in gauged settings. The paper also demonstrates a non-extremal deformation of the line element that preserves a first-order structure, illustrating how non-extremal branes can be embedded within the same flow framework. Overall, these results broaden the understanding of extremal and near-extremal black branes in gauged supergravity and their potential holographic applications, including connections to condensed matter systems via AdS/CMT.

Abstract

We study static black brane solutions in the context of N = 2 U(1) gauged supergravity in four dimensions. Using the formalism of first-order flow equations, we construct novel extremal black brane solutions including examples of Nernst branes, i.e. extremal black brane solutions with vanishing entropy density. We also discuss a class of non-extremal generalizations which is captured by the first-order formalism.

Figures (3)

• Figure 1: Interpolating solutions for ${\rm Re}\,Y^1$ and ${\rm Im}\, Y^0$.
• Figure 2: Interpolating solutions for ${\rm e}^A$ and ${\rm e}^U$.
• Figure 3: Interpolating solutions for ${\rm e}^\psi$ and $\gamma$.