Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions

Abstract

We use localization techniques to calculate the Euclidean partition functions for $\mathcal{N}=1$ theories on four-dimensional manifolds $M$ of the form $S^1\times M_3$, 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 connections.

50 pages; typos corrected, references added

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• Localization on Hopf surfaces
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Cited by in corpus (6)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Holographic renormalization and supersymmetry
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• Supersymmetric counterterms from new minimal supergravity
• Supersymmetric index on T^2 x S^2 and elliptic genus
• On N=1 partition functions without R-symmetry