Five-dimensional Nernst branes from special geometry

TL;DR

This paper constructs five-dimensional Nernst brane solutions in supergravity, showing how they resolve four-dimensional singularities and relate to boosted D3-branes, with implications for holography and string theory embedding.

Contribution

It introduces new five-dimensional Nernst brane solutions in supergravity and demonstrates their relation to four-dimensional solutions, resolving UV singularities via dimensional uplift.

Findings

Five-dimensional Nernst branes with zero entropy density constructed.

Dimensional uplift resolves four-dimensional UV singularities.

Solutions asymptote to AdS5 and relate to boosted D3-branes.

Abstract

We construct Nernst brane solutions, that is black branes with zero entropy density in the extremal limit, of FI-gauged minimal five-dimensional supergravity coupled to an arbitrary number of vector multiplets. While the scalars take specific constant values and dynamically determine the value of the cosmological constant in terms of the FI-parameters, the metric takes the form of a boosted AdS Schwarzschild black brane. This metric can be brought to the Carter-Novotny-Horsky form that has previously been observed to occur in certain limits of boosted D3-branes. By dimensional reduction to four dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863 and show how the five-dimensional lift resolves all their UV singularities. The dynamics of the compactification circle, which expands both in the UV and in the IR, plays a crucial role. At asymptotic infinity, the curvature singularity of the four-dimensional metric and the run-away behaviour of the four-dimensional scalar combine in such a way that the lifted solution becomes asymptotic to AdS5. Moreover, the existence of a finite chemical potential in four dimensions is related to fact that the compactification circle has a finite minimal value. While it is not clear immediately how to embed our solutions into string theory, we argue that the same type of dictionary as proposed for boosted D3-branes should apply, although with a lower amount of supersymmetry.