Superconformal Indices for ${\cal N}=6$ Chern Simons Theories

TL;DR

The paper tests the ABJM duality by computing the N=6 superconformal index in two regimes: a field-theory calculation at large N with k → ∞ (lambda effectively small) and a gravity calculation in AdS4 × S7/Zk at large N and large lambda. Both approaches yield the same index, expressible as a finite product I^W that counts states annihilated by at least two supercharges, thereby providing a nontrivial check of the duality in the ’t Hooft limit. The analysis shows the index is invariant under deformations of lambda in this scaling regime and discusses finite-k generalizations and implications for black hole physics and possible integrable structures at strong coupling.

Abstract

Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we perform the one loop computation that determines the field theory superconformal index of this theory and compare with the index computed over the Fock space of dual supersymmetric gravitons. In the appropriate limit (large $N$ and large $k$) we find a perfect match.