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

Abstract

We provide evidences for the duality between N=6 U(M) 4 ×U(N) ?4 Chern-Simons matter theory and N=5 O(M ^ ) 2 ×USp(2N ^ ) ?1 theory for a suitable M ^ ,N ^ 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 ×USp(2N) ?k and show that it exactly matches with the gravity index on AdS 4 ×S 7 /D k , which further provides additional evidence for the duality between the N=5 and N=6 theory for k=1.