New and old N=8 superconformal field theories in three dimensions

TL;DR

This paper reveals an infinite family of N=6 superconformal theories in three dimensions that possess hidden N=8 symmetry and parity at the quantum level, differing from previously known theories, and tests dualities via superconformal indices.

Contribution

The paper identifies a new family of N=6 superconformal Chern-Simons-matter theories with hidden N=8 symmetry, distinct from known models, and provides evidence for dualities through index comparisons.

Findings

Existence of an infinite family with hidden N=8 symmetry

Quantum-level parity invariance in these theories

Support for dualities via superconformal index comparisons

Abstract

We show that an infinite family of N=6 d=3 superconformal Chern-Simons-matter theories has hidden N=8 superconformal symmetry and hidden parity on the quantum level. This family of theories is different from the one found by Aharony, Bergman, Jafferis and Maldacena, as well as from the theories constructed by Bagger and Lambert, and Gustavsson. We also test several conjectural dualities between BLG theories and ABJ theories by comparing superconformal indices of these theories.