Index from a point
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911438921007104 |
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| author | Kang, Monica Jinwoo Lawrie, Craig Song, Jaewon |
| author_facet | Kang, Monica Jinwoo Lawrie, Craig Song, Jaewon |
| contents | We propose an algebro-geometric interpretation of the Schur and Macdonald indices of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs). We conjecture that there exists an affine scheme $X$, which reduces to the Higgs branch as a variety, such that the Hilbert series of the (appropriately-graded) arc space of its polynomial ring $J_\infty(\mathbb{C}[X])$ encodes the indices. Distinct local descriptions of a (singular) point correspond to distinct choices of $X$, giving rise to families of $\mathcal{N}=2$ SCFTs each without a Higgs branch. These local descriptions directly translate into nilpotency relations in the operator product expansions. We test our conjecture across a variety of (generalized) Argyres--Douglas theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Index from a point Kang, Monica Jinwoo Lawrie, Craig Song, Jaewon High Energy Physics - Theory Algebraic Geometry Representation Theory We propose an algebro-geometric interpretation of the Schur and Macdonald indices of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs). We conjecture that there exists an affine scheme $X$, which reduces to the Higgs branch as a variety, such that the Hilbert series of the (appropriately-graded) arc space of its polynomial ring $J_\infty(\mathbb{C}[X])$ encodes the indices. Distinct local descriptions of a (singular) point correspond to distinct choices of $X$, giving rise to families of $\mathcal{N}=2$ SCFTs each without a Higgs branch. These local descriptions directly translate into nilpotency relations in the operator product expansions. We test our conjecture across a variety of (generalized) Argyres--Douglas theories. |
| title | Index from a point |
| topic | High Energy Physics - Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2507.12510 |