Exactly marginal deformations and global symmetries

By D. Green, Z. Komargodski, N. Seiberg, Yuji Tachikawa, B. Wecht. 2010

236 citations recorded by the source corpus.

We study the problem of finding exactly marginal deformations of $ \mathcal{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 $ \mathcal{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 $ \mathcal{N} = 2 $ theories in three dimensions.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3904bfbcfa29b5b2d78f8761896a0b4c2a6d3a93

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Citations in the corpus

N=1 theories of class S_k (2015, methodology): “In particular, we can count the difference between marginal parameters and broken U(1) symmetries [28].”
T-branes and monodromy (2010, methodology): “With terminology as in [35] for example, we will refer to superpotential and Kähler potential deformations to denote chiral and non-chiral deformations of these possibly non-Lagrangian theories.”
Deformations of superconformal theories (2016, methodology): “As was shown in [16], marginal deformations are exactly marginal if and only if they do not break any flavor symmetries.”
3-Manifolds and 3d Indices (2011, background): “By the results of [66], this indicates that at least one linear combination of the 12 operators is exactly marginal.”
Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations (2015, background): “By the arguments of [34] these can only be either exactly marginal or marginally irrelevant at a SCFT without free fields.”
Four-dimensional SCFTs from M5-branes (2012, methodology): “We can compute the dimension of the conformal manifold via the method of Leigh and Strassler [49] (or equivalently [50]).”
The constraints of conformal symmetry on RG flows (2011, background): “1)), and one can prove that it always has a positive sign [35].”
Correlation functions of Coulomb branch operators (2016, background): “(8)Here is an argument along the lines of [34].”
Sphere partition functions and the Zamolodchikov metric (2014, background): “8 The origin of this difference is as follows: as explained in [40], a marginal operator can cease to be exactly marginal if there is a dimension d − 2 real multiplet that can “eat” our marginal operator and thereby become a longer multiplet.”