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

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

2008-01-09

arxiv.org/abs/0801.1435v2

JHEP 0802:064,2008

Physics

High Energy Physics

High Energy Physics - Theory

a small typo corrected, 46 pages

Scientific paper

10.1088/1126-6708/2008/02/064

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. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.

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