A note on the entanglement entropy of primary fermion fields in JT gravity

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