Exactly Marginal Deformations and Global Symmetries

Details Exactly Marginal Deformations and Global Symmetries Exactly Marginal Deformations and Global Symmetries

2010-05-19

arxiv.org/abs/1005.3546v2

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 2 figures

Scientific paper

10.1007/JHEP06(2010)106

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.

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