Spatial entanglement in two dimensional QCD: Renyi and Ryu-Takayanagi entropies

TL;DR

This paper derives a formula for the replica partition function in interacting fermionic theories and applies it to analyze spatial entanglement in 2D QCD, connecting quantum entanglement measures with holographic geometries.

Contribution

It introduces a general approach to compute the replica partition function for interacting fermions and links entanglement entropy in 2D QCD with holographic Ryu-Takayanagi entropy.

Findings

Renyi entropy for a single interval expressed via rainbow dressed quark propagator.

Order ${ m O}(1)$ contributions from mesonic T-matrix, no change to central charge.

Agreement between entanglement entropy and holographic Ryu-Takayanagi entropy.

Abstract

We derive a general formula for the replica partition function in the vacuum state, for a large class of interacting theories with fermions, with or without gauge fields, using the equal-time formulation on the light front. The result is used to analyze the spatial entanglement of interacting Dirac fermions in two-dimensional QCD. A particular attention is paid to the issues of infrared cut-off dependence and gauge invariance. The Renyi entropy for a single interval, is given by the rainbow dressed quark propagator to order ${\cal O}(N_c)$. The contributions to order ${\cal O}(1)$, are shown to follow from the off-diagonal and off mass-shell mesonic T-matrix, with no contribution to the central charge. The construction is then extended to mesonic states on the light front, and shown to probe the moments of the partonic PDFs for large light-front separations. In the vacuum and for small and large intervals, the spatial entanglement entropy following from the Renyi entropy, is shown to be in agreement with the Ryu-Takayanagi geometrical entropy, using a soft-wall AdS$_3$ model of two-dimensional QCD.