Orbifold Indices in Four Dimensions

Antonio Pittelli

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arXiv · 2403.12318

Orbifold Indices in Four Dimensions

Antonio Pittelli

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Abstract

We introduce supersymmetric indices for four-dimensional gauge theories defined on $\mathscr O \times S^1$, where $\mathscr O $ is a circle bundle over the weighted complex projective line informally known as spindle. Trivial fibrations yield a four-dimensional version of the spindle index, which we obtain by applying localization to partition functions of theories on the direct product of a spindle and a two-dimensional torus. Conversely, non-trivial fibrations lead to the branched lens index, which we compute by localizing theories on the direct product of a circle and a branched covering of the lens space, possibly endowed with conical singularities. The branched lens index encompasses the maximally refined four-dimensional lens index as a special case.

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Antonio Pittelli. 2024-03-18. Orbifold Indices in Four Dimensions. https://arxiv.org/abs/2403.12318

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