The N=1\mathcal{N}=1 Chiral Multiplet on T2×S2T^2\times S^2 and Supersymmetric Localization

Nov 11, 2013
38 pages
Published in:
  • JHEP 03 (2014) 040
  • Published: 2014
e-Print:
Report number:
  • WIS-12-13-OCT-DPPA

Citations per year

2013201620192022202505101520
Abstract: (arXiv)
We compute the supersymmetric partition function of an N=1\mathcal{N}=1 chiral multiplet coupled to an external Abelian gauge field on complex manifolds with T2×S2T^2 \times S^2 topology. The result is locally holomorphic in the complex structure moduli of T2×S2T^2\times S^2. This computation illustrates in a simple example some recently obtained constraints on the parameter dependence of supersymmetric partition functions. We also devise a simple method to compute the chiral multiplet partition function on any four-manifold M4\mathcal{M}_4 preserving two supercharges of opposite chiralities, via supersymmetric localization. In the case of M4=S3×S1\mathcal{M}_4=S^3\times S^1, we provide a path integral derivation of the previously known result, the elliptic gamma function, which emphasizes its dependence on the S3×S1S^3 \times S^1 complex structure moduli.
Note:
  • 39 pages. v2: reference added; v3: corrected typos, JHEP version
  • Topological Field Theories
  • Supergravity Models
  • Field Theories in Lower Dimensions
  • multiplet: chiral
  • multiplet: coupling
  • gauge field theory: abelian
  • partition function
  • supersymmetry
  • localization
  • moduli