Positive energy in conformal field theory
| When |
Nov 10, 2026
from 02:30 to 03:30 |
|---|---|
| Where | Salle M7.101 |
| Contact Name | Livine Etera |
| Attendees |
Jeremy Mann |
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Mardi 10 Novembre 2026
Title: Positive energy in conformal field theory
Jeremy Mann (Polytechnique)
Abstract:
Positive energy is a fundamental ingredient of non-perturbative quantum field theory: it ensures that the Euclidean time evolution operator is bounded and that correlation functions extend analytically from real to complex times. While conformal symmetry and unitarity greatly expand the cone of positive symmetry generators, the implications for correlation functions are not fully understood beyond Euclidean space. In this talk, I will use the representation theory of complex semigroups to establish a large domain of analyticity of correlation functions and a geometric criterion for the convergence of the operator product expansion. In combination with microcausality, I prove crossing symmetry relations and use them to derive universal properties of the low-energy spectrum. Time permitting, I will also discuss recent conjectures that the positive energy cone extends to certain timelike conformal Killing vectors whose positivity does not follow from unitarity.
Positive energy is a fundamental ingredient of non-perturbative quantum field theory: it ensures that the Euclidean time evolution operator is bounded and that correlation functions extend analytically from real to complex times. While conformal symmetry and unitarity greatly expand the cone of positive symmetry generators, the implications for correlation functions are not fully understood beyond Euclidean space. In this talk, I will use the representation theory of complex semigroups to establish a large domain of analyticity of correlation functions and a geometric criterion for the convergence of the operator product expansion. In combination with microcausality, I prove crossing symmetry relations and use them to derive universal properties of the low-energy spectrum. Time permitting, I will also discuss recent conjectures that the positive energy cone extends to certain timelike conformal Killing vectors whose positivity does not follow from unitarity.