Indices for Superconformal Field Theories in 3,5 and 6 Dimensions

Understand

We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4.

• We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e.
• quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras.
• Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit.