Abstract
We compute the supersymmetric partition function of an \( \mathcal{N} \) = 1 chiral multiplet coupled to an external Abelian gauge field on complex manifolds with T 2 × S 2 topology. The result is locally holomorphic in the complex structure moduli of T 2 × 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 \( \mathcal{M} \) 4 preserving two supercharges of opposite chiralities, via supersymmetric localization. In the case of \( \mathcal{M} \) 4 = S 3 × S 1, we provide a path integral derivation of the previously known result, the elliptic gamma function, which emphasizes its dependence on the S 3 × S 1 complex structure moduli.
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Closset, C., Shamir, I. The \( \mathcal{N} \) = 1 Chiral Multiplet on T 2 × S 2 and Supersymmetric Localization. J. High Energ. Phys. 2014, 40 (2014). https://doi.org/10.1007/JHEP03(2014)040
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DOI: https://doi.org/10.1007/JHEP03(2014)040