Entwinement in discretely gauged theories

• Published in: The journal of high energy physics Vol. 2016; no. 12; pp. 1 - 26
• Main Authors: Balasubramanian, V., Bernamonti, A., Craps, B., De Jonckheere, T., Galli, F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2016; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Computation; Coupling; Elementary Particles; Entanglement; Field theory; Gages; Geodesy; High energy physics; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Wavefunctions; AdS-CFT Correspondence; Gauge-gravity correspondence; Gauge Symmetry; Long strings
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2016)094

A bstract 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.