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

Abstract

We provide evidences for the duality between N = 6 U(M)(4) x U(N)(-4) Chern-Simons matter theory and N = 5 O((M) over cap)(2) x U Sp(2 (N) over cap)(-1) theory for a suitable (M) over cap, (N) over cap by working out the superconformal index, which shows perfect matching. For N = 5 theories, we show that supersymmetry is enhanced to 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) x U Sp(2N)(-k) and show that it exactly matches with the gravity index on AdS(4) x S-7/D-k, which further provides additional evidence for the duality between the N = 5 and N = 6 theory for k = 1.