  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.
