On quantum entanglement and deformations of chiral fermions

Abstract

In this thesis we review the results of [1] which study the intersection of two subjects within two-dimensional conformal field theory. The first relates to quantum entanglement of free massless fermions, while the second concerns the $T\overline T$ deformation of these free massless fermions.We start within the framework of algebraic quantum field theory emphasizing the Reeh-Schlieder theorem. We also focus on the modular flow and the modular Hamiltonian within the framework of Tomita-Takesaki theory. We revisit the modular data and the entanglement entropy for theories where the entangling region is generalized to a union of disjoint intervals. We specifically examine theories in which the entangling region is a line and a unit circle in both vacuum and thermal state.Then, we proceed to study conformal field theory on the torus to deform the free fermion confined to a unit circle at finite temperature. We study both the local and bi-local contributions to the entanglement entropy of the $T\overline T$-deformed theory.