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

TL;DR

The paper uncovers a quantum enhancement to ${\mathcal N}=8$ supersymmetry in a class of ${\mathcal N}=6$ 3D Chern-Simons-matter theories, specifically ABJ theories with $M=N{+}1$ and $k=\pm2$, and reveals hidden parity via dualities. It analyzes the moduli space to identify when such enhancement can occur, showing that only $|k|=1,2$ with $M-N\le |k|$ permit ${\mathcal N}=8$, and highlights a self-dual, parity-symmetric case at $M-N=1$, $k=2$. The authors construct protected $\Delta=1$ monopole scalars in ${\bf 10}_{-1}$ that organize into $Spin(8)$ currents, proving hidden ${\mathcal N}=8$ and revealing a quantumly free ${\mathcal N}=8$ sector that leads to a doubled supercurrent multiplet. They employ the superconformal index, computed via localization, to distinguish theories with identical moduli spaces (ABJM/ABJ/BLG) and to test dualities, finding precise matches in certain BLG-ABJ/ABJM pairs while ruling out isomorphisms in others, thus refining the landscape of 3D ${\mathcal N}=8$ SCFTs and their M-theory interpretations.

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.