Exactly Marginal Deformations and Global Symmetries

TL;DR

This paper characterizes the space of exactly marginal deformations in 4D N=1 superconformal field theories, linking it to global symmetries and group theory, and extends the analysis to N=2 theories in three dimensions.

Contribution

It provides a group-theoretic framework for identifying exactly marginal deformations and clarifies their relation to global symmetries, extending previous work by Leigh and Strassler.

Findings

Exactly marginal operators are related to conserved current multiplets.

The conformal manifold is the quotient of marginal couplings by the complexified global symmetry group.

The method simplifies the enumeration of exactly marginal deformations.

Abstract

We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a conserved current multiplet. Additionally, we find that the space of exactly marginal deformations, also called the "conformal manifold," is the quotient of the space of marginal couplings by the complexified continuous global symmetry group. This fact explains why exactly marginal deformations are ubiquitous in N=1 theories. Our method turns the problem of enumerating exactly marginal operators into a problem in group theory, and substantially extends and simplifies the previous analysis by Leigh and Strassler. We also briefly discuss how to apply our analysis to N=2 theories in three dimensions.