Localization on Hopf surfaces

Benjamin Assel*, Davide Cassani, Dario Martelli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

96 Citations (Scopus)

Abstract

We discuss localization of the path integral for supersymmetric gauge theories with an R-symmetry on Hermitian four-manifolds. After presenting the localization locus equations for the general case, we focus on backgrounds with S-1 x S-3 topology, admitting two supercharges of opposite R-charge. These are Hopf surfaces, with two complex structure moduli p, q. We compute the localized partition function on such Hopf surfaces, allowing for a very large class of Hermitian metrics, and prove that this is proportional to the supersymmetric index with fugacities p, q. Using zeta function regularisation, we determine the exact proportionality factor, finding that it depends only on p, q, and on the anomaly coefficients a, c of the field theory. This may be interpreted as a supersyrnmetric Casimir energy, and provides the leading order contribution to the partition function in a large N expansion.

Original languageEnglish
Article number123
Number of pages56
JournalJournal of High Energy Physics
Volume2014
Issue number8
DOIs
Publication statusPublished - 1 Aug 2014

Keywords

  • Supersymmetric gauge theory
  • Matrix Models
  • SUPERSYMMETRIC GAUGE-THEORIES
  • N=1 SUPERGRAVITY
  • GAMMA-FUNCTION
  • FIELD-THEORIES
  • STRESS TENSOR
  • ANOMALIES
  • CALCULUS
  • INDEX

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