Séminaire d'Analyse

Two-point functions of Conformal Field Theory and Conical Singularities

par Jiasheng Lin (IMJ-PRG)

Europe/Paris
Salle Pellos (1R2-207)

Salle Pellos (1R2-207)

Description

In this talk we describe the imminently coming work in collaboration with B. Estienne where we demonstrate a purely mathematical construction which recovers some results of Cardy and Calabrese on the so-called entanglement entropy. Skipping briefly over introducing the latter notion, we start by defining mathematically a Conformal Field Theory over a (smooth) Riemann surface (Σ,g) and its partition function as well as correlation functions. Then for a Riemann surface with "conical singularities" we will define the CFT “partition function” (denoted Z) on it using a simple Hadamard renormalization (removing disks) of the Polyakov anomaly integral, a first main ingredient of the work. Then we state the main result namely for a branched cover f:ΣdΣ of degree d, the ratio Z(Σd,fg)/Z(Σ,g)d of partition functions transforms under conformal changes of g like a two-point function of CFT primary operators of specific conformal weights. If time permits, we talk briefly about the physical motivation around entanglement entropies.