Long Strings and Quasinormal Winding Modes

TL;DR

This paper analyzes the spectral properties of particles and strings in BTZ black hole backgrounds, revealing long string modes and quasinormal winding modes through path integral and orbifold techniques.

Contribution

It introduces a novel method to compute the particle path integral on SL(2,R) and relates it to string spectral content in BTZ backgrounds, highlighting long string and quasinormal modes.

Findings

Identification of poles corresponding to long string modes.

Relation of poles to quasinormal winding modes.

Connection between Lorentzian orbifolds and Euclidean BTZ partition functions.

Abstract

We compute the path integral for a particle on the covering group of SL(2,R) using a decomposition of the Lie algebra into adjoint orbits. We thus intuitively derive the Hilbert space of the particle on the group including discrete and continuous representations. Next, we perform a Lorentzian hyperbolic orbifold of the partition function and relate it to the Euclidean BTZ partition function. We use the particle model to inform further discussion of the spectral content of the one loop vacuum amplitude for strings on BTZ black hole backgrounds. We argue that the poles in the loop integrand code contributions of long string modes that wind the black hole. We moreover identify saddle point contributions of quasinormal winding modes.