Marginal Deformations and 3-Algebra Structures

TL;DR

This paper investigates marginal deformations in superconformal Chern-Simons theories based on 3-algebras, introducing a new 3-product concept and analyzing their effects on the BLG and ABJM models.

Contribution

It introduces the notion of an associated 3-product for gauge invariant deformations and computes two-loop beta functions confirming marginality of certain deformations.

Findings

Confirmed conformal invariance of BLG and ABJM models.

Verified beta-deformations of ABJM are marginal at two loops.

Established a general framework for gauge invariant deformations using 3-products.

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.