Generalized replica manifolds. Part I. Surgery and averaging
- 1University of Kentucky
Abstract
A bstract : 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 subregions, 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. Finally, we discuss how this framework looks in the context of large- N theories and holography, with a bird’s-eye view of potential future directions. This paper focuses on averaging over operators that form a representation of the Heisenberg group; a subsequent paper will focus on how we can extend this framework to more general operator averaging.
Related
- Replica Analysis of Overfitting in Vector Generalized Linear Models
- GLSMs for non-polynomial deformations and generalized complete intersection Calabi-Yau manifolds
- Generalized Symmetries of QED4 on Non-Spin Manifolds
- Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N−1/2) in the Replica Symmetric Phase
- Moments of Random Permanents and Hafnians: A Replica Approach
BibTeX
@article{radwan2026generalized,
title = {{Generalized replica manifolds. Part I. Surgery and averaging}},
author = {Mohamed Hany Radwan},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)023},
url = {https://link.springer.com/10.1007/JHEP10(2026)023},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Generalized replica manifolds. Part I. Surgery and averaging
AU - Mohamed Hany Radwan
PY - 2026
DA - 2026/10/02
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)023
UR - https://link.springer.com/10.1007/JHEP10(2026)023
AB - A bstract : 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 subregions, 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. Finally, we discuss how this framework looks in the context of large- N theories and holography, with a bird’s-eye view of potential future directions. This paper focuses on averaging over operators that form a representation of the Heisenberg group; a subsequent paper will focus on how we can extend this framework to more general operator averaging.
SN - 1029-8479
ER -