A Note on Entanglement Entropy for Primary Fermion Fields in JT Gravity

TL;DR

This paper investigates entanglement entropy of primary fermion fields in 2D JT gravity, employing resolvent techniques to derive results without relying on conformal field theory methods.

Contribution

It introduces a resolvent-based approach to compute entanglement entropy for fermions in JT gravity, avoiding traditional CFT techniques.

Findings

Derived the two-point correlators of primary fermions in JT spacetime.

Calculated the renormalized entanglement entropy for massless Dirac fields.

Presented a standard resolvent method as an alternative to CFT approaches.

Abstract

In this paper we analyse and discuss 2D Jackiw-Teitelboim (JT) gravity coupled to primary fermion fields in asymptotically anti-de Sitter (AdS) spacetimes. We get a particular solution of the massless Dirac field outside the extremal black hole horizon and find the solution for the dilaton in JT gravity. Two dimensional JT gravity spacetime is conformally flat, we calculate the two point correlators of primary fermion fields under the Weyl transformations. The key point of this work is to present a standard technique which is called resolvent rather than CFT methods. We redefine the fields in terms of the conformal factor as the fermion fields, and we use the resolvent technique to derive the renormalized entanglement entropy for massless Dirac fields in JT gravity.