Abstract
We use localization techniques to calculate the Euclidean partition functions for \( \mathcal{N} \) = 1 theories on four-dimensional manifolds M of the form S 1 × M 3, where M 3 is a circle bundle over a Riemann surface. These are generalizations of the \( \mathcal{N} \) = 1 indices in four-dimensions including the lens space index. We show that these generalized indices are holomorphic functions of the complex structure moduli on M. We exhibit the deformation by background flat connection.
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Nishioka, T., Yaakov, I. Generalized indices for \( \mathcal{N} \) = 1 theories in four-dimensions. J. High Energ. Phys. 2014, 150 (2014). https://doi.org/10.1007/JHEP12(2014)150
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DOI: https://doi.org/10.1007/JHEP12(2014)150