Two applications of the analytic conformal bootstrap: A quick tour guide

TL;DR

This paper reviews recent analytic conformal bootstrap methods and demonstrates their applications in studying the epsilon expansion of the Wilson Fisher model and the large N expansion of maximally supersymmetric Super Yang Mills theory.

Contribution

It provides a concise overview of analytic bootstrap techniques and applies them to two significant models in conformal field theory, highlighting new analytical approaches.

Findings

Dispersion relation aids epsilon expansion analysis

Large N expansion insights for supersymmetric theories

Enhanced understanding of conformal bootstrap applications

Abstract

We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $\epsilon$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions.