NB: non-standard day and time.

 

Title: Generalized Replica Manifolds: The Tailor's Guide to Entanglement  

 

Abstract: We develop a simple framework for implementing a type of path integral "surgery" through a correlated averaging over codimension-one defects/extended operators. This technique is then used to construct replica manifolds by effectively cutting and gluing the path integral without explicitly modifying the underlying manifold. We argue that restricted forms of this averaging may be used to calculate Rényi entanglement entropy corresponding to a wide range of choices of subsystem partitioning. When the entanglement entropy being calculated in this way does not simply correspond to entanglement between sub-regions, we call the resulting objects from this surgery ``generalized replica manifolds.'' We show how this framework extends to gauge theories and, in particular, how in non‑Abelian gauge theories it establishes a connection between replica calculations of a gauge invariant notion of entanglement between color degrees of freedom and a quiver gauge theory structure. We also discuss further extensions of this framework as well as potential application to large N models and holography.