Higher spin fermions in the BTZ black hole

TL;DR

This paper extends the exact solutions of wave equations to fermionic higher spin fields in the BTZ black hole, deriving quasinormal modes and confirming their consistency with AdS/CFT predictions and heat kernel calculations.

Contribution

It provides the first exact solutions for fermionic higher spin wave equations in BTZ, including quasinormal modes and 1-loop determinants, confirming duality predictions.

Findings

Exact fermionic higher spin wave solutions in BTZ

Quasinormal modes match dual CFT poles

1-loop determinant agrees with heat kernel methods

Abstract

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant in terms of the quasinormal modes and show it agrees with that obtained by integrating the heat kernel found by group theoretic methods.