Three-dimensional topologically gauged N=6 ABJM type theories

TL;DR

This paper constructs a three-dimensional $ =6$ conformal supergravity theory and couples it to the ABJM theory, deriving a complete Lagrangian with new scalar potential terms and ensuring supersymmetry invariance through detailed cancellation of variations.

Contribution

It provides the first explicit construction of topologically gauged $ =6$ ABJM theories with a fully consistent Lagrangian and transformation rules ensuring supersymmetry.

Findings

Derived the $ =6$ conformal supergravity in 3D.

Coupled supergravity to ABJM theory with supersymmetry invariance.

Identified new scalar potential terms with fewer structure constants.

Abstract

In this paper we construct the $\mathcal N=6$ conformal supergravity in three dimensions from a set of Chern-Simons-like terms one for each of the graviton, gravitino, and R-symmetry gauge field and then couple this theory to the $\mathcal N=6$ superconformal ABJM theory. In a first step part of the coupled Lagrangian for this topologically gauged ABJM theory is derived by demanding that all terms of third and second order in covariant derivatives cancel in the supersymmtry variation of the Lagrangian. To achieve this the transformation rules of the two separate sectors must be augmented by new terms. In a second step we analyze all terms in $\delta L$ that are of first order in covariant derivatives. The cancelation of these terms require additional terms in the transformation rules as well as a number of new terms in the Lagrangian. As a final step we check that all remaining terms in $\delta L$ which are bilinear in fermions cancel which means that the presented Lagrangian and transformation rules constitute the complete answer. In particular we find in the last step new terms in the scalar potential containing either one or no structure constant. The non-derivative higher fermion terms in $\delta L$ that have not yet been completely analyzed are briefly discussed.