Asymptotic Symmetries of Three-Dimensional Black Strings

TL;DR

The paper constructs a consistent phase space for three-dimensional gravity with a dilaton and form fields that encompasses black-string solutions, and identifies boundary conditions whose asymptotic charges form a centerless Virasoro algebra supplemented by three U(1) generators. It shows no BMS3 structure in this setting and derives finite, integrable charges, illustrating the symmetry algebra with explicit expressions and examples. The authors connect the charged black string and related solutions to marginal deformations of the SL(2,R)/R coset and its two-dimensional black hole seed, revealing a rich CFT interpretation and proposing new deformations that generate novel exact backgrounds. They also analyze the thermodynamics of zero-mode solutions, including a detailed first-law and Smarr relation, and discuss time-dependent saddles and future directions for holographic and string-theoretic insights.

Abstract

We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global $u(1)$ generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system.