Supersymmetric partition functions and the three-dimensional A-twist

Cyril Closset, Heeyeon Kim, Brian Willett

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


We study three-dimensional N= 2 supersymmetric gauge theories on ℳ gp, an oriented circle bundle of degree p over a closed Riemann surface, Σg. We compute the ℳ gp supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round S3 can be understood as the expectation value of a so-called “fibering operator” on S2×S1 with a topological twist. More generally, we show that the 3d N= 2 supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on ℳ gp are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimensional supersymmetric dualities.

Original languageEnglish (US)
Article number74
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Field Theories in Lower Dimensions
  • Supersymmetric Gauge Theory
  • Supersymmetry and Duality
  • Topological Field Theories


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