The (Formula Presented.) Schur index from free fermions

Jun Bourdier*, Nadav Drukker, Jan Felix

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
136 Downloads (Pure)


We study the Schur index of 4-dimensional N = 2 circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular SU (N) quivers of arbitrary length we evaluate the large N limit of the index, up to exponentially suppressed corrections. For the single node theory (N = 4 SYM) and the two node quiver we are able to go beyond the large N limit, and obtain the complete, all orders large N expansion of the index, as well as explicit finite N results in terms of elliptic functions.

Original languageEnglish
Article number167
Pages (from-to)1-33
Number of pages33
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 27 Jan 2016


  • Matrix Models
  • Supersymmetric gauge theory


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