The (Formula Presented.)  Schur index from free fermions

Jun Bourdier; Nadav Drukker; Jan Felix

doi:10.1007/JHEP01(2016)167

The (Formula Presented.) Schur index from free fermions

Jun Bourdier^*, Nadav Drukker, Jan Felix

^*Corresponding author for this work

King's College London

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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Abstract

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 language	English
Article number	167
Pages (from-to)	1-33
Number of pages	33
Journal	Journal of High Energy Physics
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1007/JHEP01(2016)167
Publication status	Published - 27 Jan 2016

Keywords

Matrix Models
Supersymmetric gauge theory

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10.1007/JHEP01(2016)167Licence: CC BY

The N = 2 Schur_BOURDIER_Published27January2016_GOLD VoR (CC-BY)Final published version, 638 KBLicence: CC BY

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N2 - 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.

AB - 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.

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KW - Supersymmetric gauge theory

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The (Formula Presented.) Schur index from free fermions

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