Orbifold Indices in Four Dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911802949894144 |
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| author | Pittelli, Antonio |
| author_facet | Pittelli, Antonio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_12318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbifold Indices in Four Dimensions Pittelli, Antonio High Energy Physics - Theory Mathematical Physics 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. |
| title | Orbifold Indices in Four Dimensions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2403.12318 |