Finite group actions on genus two $SL(2, \mathbb{C})$-character variety and applications to SCFTs
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| Format: | Preprint |
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2026
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| _version_ | 1866911498446569472 |
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| author | Arthamonov, Semeon Pribytok, Anton |
| author_facet | Arthamonov, Semeon Pribytok, Anton |
| contents | We investigate irreducible components of the fixed point sets of $ SL(2,\mathbb{C}) $-character variety of the genus two surface group under orientation preserving actions of the finite groups of the $ Mod(Σ_{2}) $. We work in the $ \mathcal{O} $-generator presentation of the genus two DAHA and its classical limit $ \mathcal{A}_{q=1,t} $, where we observe nontrivial coincidences between fixed loci attached to different subgroups and establish genus/irregularity transitions. The subvarieties obtained in this way provide novel geometric candidates for symmetry-reduced moduli spaces relevant to $ 4d $ $ \mathcal{N} = 2 $ SCFTs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite group actions on genus two $SL(2, \mathbb{C})$-character variety and applications to SCFTs Arthamonov, Semeon Pribytok, Anton Mathematical Physics High Energy Physics - Theory Group Theory Representation Theory We investigate irreducible components of the fixed point sets of $ SL(2,\mathbb{C}) $-character variety of the genus two surface group under orientation preserving actions of the finite groups of the $ Mod(Σ_{2}) $. We work in the $ \mathcal{O} $-generator presentation of the genus two DAHA and its classical limit $ \mathcal{A}_{q=1,t} $, where we observe nontrivial coincidences between fixed loci attached to different subgroups and establish genus/irregularity transitions. The subvarieties obtained in this way provide novel geometric candidates for symmetry-reduced moduli spaces relevant to $ 4d $ $ \mathcal{N} = 2 $ SCFTs. |
| title | Finite group actions on genus two $SL(2, \mathbb{C})$-character variety and applications to SCFTs |
| topic | Mathematical Physics High Energy Physics - Theory Group Theory Representation Theory |
| url | https://arxiv.org/abs/2603.07846 |