Entanglement Entropy and Conical Singularities

par M. Jiasheng Lin (Institut de maths de Jussieu)

mardi 8 avr. 2025, 14:00 → 15:00 Europe/Paris

Salle de séminaire (Orléans institut Denis Poisson)

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 $f:{\mathrm{\Sigma }}_d\to \mathrm{\Sigma }$ of degree $d$, the ratio $Z({\mathrm{\Sigma }}_d,f^{\ast }g)/Z(\mathrm{\Sigma },g{)}^d$ of partition functions transforms under conformal changes of g like a correlation function of CFT primary operators of specific conformal weights.