Entwinement in discretely gauged theories

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.

28 pages, 4 figures; v2: clarifications and reference added, minor typos corrected, published version

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• The landscape of complexity measures in 2D gravity
• Geometric Surprises in the Python's Lunch Conjecture
• Bulk quantum corrections to entwinement
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure
• Bulk reconstruction of AdS${}_{d+1}$ metrics and developing kinematic space
• Quantum Information Approaches to Quantum Gravity