GT ADG-Systèmes Dynamiques
Entanglement Entropy and Conical SingularitiesJiasheng Lin (Institut de maths de Jussieu)
Tuesday 08 April 2025 14:00 - Orléans institut Denis Poisson - Salle de séminaire
Résumé :
In this talk we describe the work (arXiv:2501.19014) in collaboration with B. Estienne where we demonstrate a purely mathematical and geometric construction which recovers some results of Cardy and Calabrese on the so-called entanglement entropy. We start by explaning briefly what are Conformal Field Theories, its path-integral formulation, and its relation to gluing surfaces. Then we introduce the entanglement entropy, and relate it to conical surfaces via the path-integral formulation. Finally we formulate the main result of the work: we define CFT "partition functions" on surfaces with conical singularities, using a "Hadamard renormalization'' of the Polyakov anomaly integral. Our result says that for a branched cover $f:\Sigma_d→\Sigma$ of degree $d$, the ratio $Z(\Sigma_d,f^*g)/Z(\Sigma,g)^d$ of partition functions transforms under conformal changes of g like a correlation function of CFT primary operators of specific conformal weights.
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