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The exact Schur index of N = 4 SYM

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number210
Pages (from-to)1-10
Number of pages10
JournalJournal of High Energy Physics
Issue number11
Accepted/In press29 Oct 2015
Published30 Nov 2015


King's Authors


The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least N=2 supersymmetry in four dimensions is a particular refinement of the index, dependent on one parameter q serving as the fugacity for a particular set of charges which commute with the hamiltonian and some supersymmetry generators. This index has a known expression for all Lagrangian and some non-Lagrangian theories as a finite dimensional integral or a complicated infinite sum. In the case of N=2 SYM with gauge group U(N) we rewrite this as the partition function of a gas of N non interacting and translationally invariant fermions on a circle. This allows us to perform the integrals and write down explicit expressions for fixed N as well as the exact all orders large N expansion.

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