Energy Correlators, Dispersive Sum Rules, and Modular Bootstrap in Conformal Field Theories

Author: Chang, Cyuan-Han

Year: 2024

Degree: Dissertation (Ph.D.)

Advisor: Simmons-Duffin, David

Committee Members: Kapustin, Anton N.; Motrunich, Olexei I.; Ooguri, Hirosi; Simmons-Duffin, David

Option: Physics

DOI: 10.7907/na45-ng05

Abstract

In this thesis, we study various observables and constraints in conformal field theories. First, we consider a product of two null-integrated operators on the same null plane and derive an operator product expansion in the direction transverse to the null plane. We then generalize to the case of three null-integrated operators, and study constraints from Lorentz symmetry. We generate a class of dispersive CFT sum rules using commutativity of null-integrated operators, and build a dictionary between the CFT sum rules and the flat space dispersion relations. Finally, we consider two-dimensional conformal field theories and derive a scalar crossing equation using modular invariance.

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