Entwinement in discretely gauged theories

TL;DR

This paper introduces entwinement, a new measure of quantum entanglement for discretely gauged theories, using a novel replica method, with applications to holography and AdS/CFT correspondence.

Contribution

It formalizes entwinement with a new replica technique involving charged twist operators, enabling the study of internal gauge degrees of freedom in quantum field theories.

Findings

Entwinement measures lengths of non-minimal geodesics in holographic duals.

Application to symmetric orbifold CFTs with $S_N$ gauging.

Reveals new fine-structure quantities of quantum wavefunctions.

Abstract

We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_N$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS$_3$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the $M=0$ BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.