Marginal Deformations and 3-Algebra Structures

Abstract

We study marginal deformations of superconformal Chern-Simons matter theories that are based on 3-algebras. For this, we introduce the notion of an associated 3-product, which captures very general gauge invariant deformations of the superpotentials of the BLG and ABJM models. We also consider conformal multi-trace deformations preserving N=2 supersymmetry. We then use N=2 supergraph techniques to compute the two-loop beta functions of these deformations. Besides confirming conformal invariance of both the BLG and ABJM models, we also verify that the recently proposed beta-deformations of the ABJM model are indeed marginal to the order we are considering.

v3: 34 pages, typos fixed and minor clarifications added

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Cited by in corpus (34)

• n-ary algebras: a review with applications
• Exactly Marginal Deformations and Global Symmetries
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Infrared Stability of N=2 Chern-Simons Matter Theories
• Infrared stability of ABJ-like theories
• N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators
• Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace
• Scattering in ABJ theories
• Effective action of three-dimensional extended supersymmetric matter on gauge superfield background
• M-brane Models from Non-Abelian Gerbes
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• N=8 Superspace Constraints for Three-dimensional Gauge Theories
• Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
• F-maximization along the RG flows: a proposal
• Low-energy effective actions in three-dimensional extended SYM theories
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• The ABJM Model is a Higher Gauge Theory
• Z Extremization in Chiral-Like Chern Simons Theories
• The Conformal Manifold of Chern-Simons Matter Theories
• Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories
• Spin chain for the deformed ABJM theory
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• On the infrared behaviour of 3d Chern-Simons theories in N=2 superspace
• Superalgebra Realization of the 3-algebras in N=6, 8 Chern-Simons-matter Theories
• The Background Field Method for N = 2, d3 Super Chern-Simons-Matter Theories
• A note on strings in deformed AdS_4 x CP3: giant magnon and single spike solutions
• Construction of New D=3, N=4 Quiver Gauge Theories
• Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
• Fusion of Superalgebras and D=3, N=4 Quiver Gauge Theories
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Superconformal Chern-Simons theories beyond leading order
• On-shell supersymmetry breaking in the Abelian Chern-Simons-matter model in three dimensions of spacetime
• Exact beta-functions in softly-broken N=2 Chern-Simons matter theories
• Renormalization Group Improvement and Dynamical Breaking of Symmetry in a Supersymmetric Chern-Simons-matter Model