Strings in AdS$_3$: one-loop partition function and near-extremal BTZ thermodynamics

TL;DR

This paper analyzes the string partition function in AdS$_3$, demonstrating how spacetime symmetries are reflected in the one-loop sum and confirming the applicability of near-extremal black hole thermodynamics at finite string length.

Contribution

It clarifies the connection between AdS$_3$ symmetries, boundary currents, and the string partition function, extending the understanding of black hole thermodynamics in string theory.

Findings

Asymptotic symmetries are captured by the one-loop partition sum.

Near-extremal black hole thermodynamics holds at finite string length.

Identification of bulk gauge fields corresponding to boundary currents.

Abstract

We revisit the computation of the string partition function in AdS$_3$ focussing on the appearance of spacetime (super) symmetries. We show how the asymptotic symmetries of the AdS$_3$ spacetime, which generate the boundary (super) Virasoro currents, are captured by the one-loop partition sum. We use this to argue that the recent understanding of near-extremal black hole thermodynamics based on the gravitational path integral continues to hold for finite string length. Along the way we clarify some aspects of the AdS$_3$/CFT$_2$ duality and, in particular, deduce which bulk gauge fields lead to boundary currents. We also explain how one can interpolate between supersymmetric and thermal (Atick-Witten) fermion boundary conditions in the target space by suitably tuning rotational chemical potentials in the string partition function.