Geometry and Phase Structure of Non-Relativistic Branes

TL;DR

This paper constructs new non-relativistic brane solutions using TsT transformations, explores their phase structures via a novel free energy calculation method, and finds many solutions exhibit asymptotic Schrödinger symmetry.

Contribution

It introduces a new, more efficient method for deriving free energy of black branes and applies it to analyze phase structures of non-relativistic string theory backgrounds.

Findings

Many solutions have asymptotic Schrödinger symmetry

The new free energy method is validated on known backgrounds

Phase transitions are analyzed in the constructed backgrounds

Abstract

We use the solution generating technique, the TsT transformation, to obtain new solutions in type II string theory as well as in M-theory. We explicitly work out examples starting with rotating D3 and M2 branes as well as D1-D5-p system. Among a variety of solutions, we find many of them have asymptotic Schr\"odinger symmetry. We also device a new method of deriving free energy of black brane systems, which is more efficient than the Euclidean action procedure. We test our method on known examples before applying it to new asymptotically Schr\"odinger backgrounds. We study phase structure of these backgrounds by analysing the free energy thus derived.