Year: 2025
Type: preprint
Abstract: This note presents a purely geometric construction of the so-called twist-field correlation functions in Conformal Field Theory (CFT), derived from conical singularities. This approach provides a purely mathematical interpretation of the seminal results in physics by Cardy and Calabrese on the entanglement entropy of quantum systems. Specifically, we begin by defining CFT partition functions on surfaces with conical singularities, using a ``Cauchy-Hadamard renormalization'' of the Polyakov anomaly integral. Next, we demonstrate that for a branched cover $f:Σ_d\to Σ$ with $d$ sheets, where the cover inherits the pullback of a smooth metric from the base, a specific ratio of partition functions on the cover to the base transforms under conformal changes of the base metric in the same way as a correlation function of CFT primary fields with specific conformal weights. We also provide a discussion of the physical background and motivation for entanglement entropy, focusing on path integrals and the replica trick, which serves as an introduction to these ideas for a mathematical audience.
Source: arXiv (Cornell University)
Authors: Estienne, Benoit, Lin, Jiasheng
Institution: Sorbonne Université
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407090944