Asymptotic counting of BPS operators in superconformal field theories
arXiv:0802.3015 · doi:10.1063/1.2970775
Abstract
We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For non-zero coupling, the corresponding multi-variable partition functions can be written in terms of generating functions for vector partitions or their weighted generalisations. We derive asymptotics for the density of states for a wide class of such multi-variable partition functions. We also point out a particular factorisation property of the finite N partition functions. Finally, we discuss the concept of a limit curve arising from the large N partition functions, which is related to the notion of a typical state and discuss some implications for the holographic duals.
arXiv comment39 pages latex. v2: minor improvements, reference added
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- Asymptotic degeneracies of M2-brane SCFTs