Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities

TL;DR

This review discusses how conformal field theory techniques are applied to perturbative calculations in N=4 Super Yang-Mills and ABJM theories, highlighting recent advances in amplitudes, correlators, and Wilson loops.

Contribution

It provides a comprehensive overview of conformal methods in perturbative superconformal theories, including new results on Wilson loops and three-point functions.

Findings

Analysis of light-like polygonal Wilson loops in ABJM theory.

Calculation of three-point functions involving BPS and twist-two operators.

Relations established between amplitudes, correlators, and Wilson loops.

Abstract

This review covers a number of applications of conformal field theory methods for perturbative calculations in N=4 Super Yang-Mills and ABJM theory. After motivating the role of superconformal symmetry for elementary particle physics research, we review some basic facts about conformal symmetry and conformal transformations of fields in a pedagogical manner. The implications for perturbative quantum field theory calculations are discussed in terms of Ward identities. Recent developments and relations between amplitudes, correlators and Wilson loops are reviewed for N=4 Super Yang-Mills as well as ABJM theory. We give more details on previously published results on light-like polygonal Wilson loops in ABJM theory as well as the calculation of three-point functions of two BPS and one twist-two operator in N=4 Super Yang-Mills theory.