• DOI:10.1088/1126-6708/2008/02/064
• Corpus ID: 133713

Indices for superconformal field theories in 3, 5 and 6 dimensions

@article{Bhattacharya2008IndicesFS,
  title={Indices for superconformal field theories in 3, 5 and 6 dimensions},
  author={Jyotirmoy Bhattacharya and Sayantani Bhattacharyya and Shiraz Minwalla and S. Raju},
  journal={Journal of High Energy Physics},
  year={2008},
  volume={2008},
  pages={064-064}
}

• J. Bhattacharya, Sayantani Bhattacharyya, +1 author S. Raju
• Published 9 January 2008
• Mathematics
• Journal of High Energy Physics

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.