Relative Entropy and Torsion Coupling

TL;DR

This paper investigates the positivity of relative entropy in a holographic conformal field theory deformed by a fermionic operator, deriving constraints on torsion coupling and fermion properties through Einstein-Cartan gravity.

Contribution

It provides a novel perturbative analysis of relative entropy in a holographic setting with torsion, linking quantum information measures to gravitational couplings.

Findings

Positivity of relative entropy constrains axial current-torsion coupling.

Derived bounds on fermion mass and equation of state.

Established a connection between quantum entanglement and torsion in gravity.

Abstract

We evaluate the relative entropy on a ball region near the UV fixed point of a holographic conformal field theory deformed by a fermionic operator of nonzero vacuum expectation value. The positivity of the relative entropy considered here is implied by the expected monotonicity of decrease of quantum entanglement under RG flow. The calculations are done in the perturbative framework of Einstein-Cartan gravity in four-dimensional asymptotic anti-de Sitter space with a postulated standard bilinear coupling between axial fermion current and torsion. By requiring positivity of relative entropy, our result yields a constraint on axial current-torsion coupling, fermion mass and equation of state.