Definitions of entwinement

TL;DR

This paper constructs a lattice model of symmetric product orbifold CFTs to define and compute entwinement, aligning with holographic results and clarifying its meaning in specific string configurations.

Contribution

It provides a discretized, gauge-invariant definition of entwinement that matches holographic calculations, clarifying its interpretation within symmetric product orbifold CFTs.

Findings

Constructed a gauge-invariant reduced density matrix for entwinement

Demonstrated agreement between lattice model entropy and holographic entwinement

Clarified the meaning of entwinement for intervals within long strings

Abstract

Entwinement was first introduced as the CFT dual to extremal, non-minimal geodesics of quotiented AdS$_3$ spaces. It was heuristically meant to capture the entanglement of internal, gauged degrees of freedom, for instance in the symmetric product orbifold CFT of the D1/D5 brane system. The literature now contains different, and sometimes inequivalent, field theory definitions of entwinement. In this paper, we build a discretized lattice model of symmetric product orbifold CFTs, and explicitly construct a gauge-invariant reduced density matrix whose von Neumann entropy agrees with the holographic computation of entwinement. Refining earlier notions, our construction gives meaning to the entwinement of an interval of given size within a long string of specific length. We discuss similarities and differences with previous definitions of entwinement.