Relative Entropy and Torsion Coupling

TL;DR

The paper studies how the information-theoretic property of relative entropy constrains a holographic CFT deformed by a fermionic operator that sources bulk torsion via an axial current–torsion coupling. Using a perturbative Einstein–Cartan setup in AdS4 and turning on fermionic zero modes, the authors compute the bulk backreaction up to second order and evaluate the holographic relative entropy for a ball region near the UV fixed point. They show that positivity of the second-order relative entropy yields a bound m^2 ell^2 ≥ 2 eta_t^2 / mu0^2, linking the bulk fermion mass, torsion coupling, and the equation-of-state parameter; if eta_t=0, no bound arises, which is consistent with the absence of torsion backreaction. The work demonstrates how quantum information inequalities can impose nontrivial constraints on torsion gravity and deformed holographic CFTs, and suggests a bulk energy-condition interpretation with possible swampland implications for torsion couplings.

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.