Duality between N=5 and N=6 Chern-Simons matter theory

TL;DR

This paper provides evidence for a duality between certain N=5 and N=6 supersymmetric Chern-Simons theories by matching superconformal indices and demonstrating supersymmetry enhancement, supported by gravity dual calculations.

Contribution

It explicitly constructs monopole operators to show supersymmetry enhancement and matches large N indices with gravity duals, strengthening the duality between N=5 and N=6 theories.

Findings

Superconformal indices match between dual theories.

Supersymmetry in N=5 theories enhances to N=6.

Large N index matches gravity dual predictions.

Abstract

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$