Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918266210877440 |
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| author | Hanson, Robert |
| author_facet | Hanson, Robert |
| contents | Using geometric Eisenstein series, foundational work of Arinkin and Gaitsgory constructs cuspidal-Eisenstein decompositions for ind-coherent nilpotent sheaves on the de Rham moduli of local systems. This article extends these constructions to coherent (not ind-coherent) nilpotent sheaves on the Dolbeault, Hodge and twistor moduli from non-abelian Hodge theory. We thus account for Higgs bundles, Hodge filtrations and hyperkähler rotations of local systems. In particular, our constructions are shown to decompose a hyperholomorphic sheaf theory of so-called BBB-branes into cuspidal and Eisenstein components. Our work is motivated, on the one hand, by the `classical limit' or `Dolbeault geometric Langlands conjecture' of Donagi and Pantev, and on the other, by attempts to interpret Kapustin and Witten's physical duality between BBB-branes and BAA-branes in 4D supersymmetric Yang--Mills theories as a mathematical statement within the geometric Langlands program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry Hanson, Robert Algebraic Geometry 14D24, 14A30, 14F08 Using geometric Eisenstein series, foundational work of Arinkin and Gaitsgory constructs cuspidal-Eisenstein decompositions for ind-coherent nilpotent sheaves on the de Rham moduli of local systems. This article extends these constructions to coherent (not ind-coherent) nilpotent sheaves on the Dolbeault, Hodge and twistor moduli from non-abelian Hodge theory. We thus account for Higgs bundles, Hodge filtrations and hyperkähler rotations of local systems. In particular, our constructions are shown to decompose a hyperholomorphic sheaf theory of so-called BBB-branes into cuspidal and Eisenstein components. Our work is motivated, on the one hand, by the `classical limit' or `Dolbeault geometric Langlands conjecture' of Donagi and Pantev, and on the other, by attempts to interpret Kapustin and Witten's physical duality between BBB-branes and BAA-branes in 4D supersymmetric Yang--Mills theories as a mathematical statement within the geometric Langlands program. |
| title | Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry |
| topic | Algebraic Geometry 14D24, 14A30, 14F08 |
| url | https://arxiv.org/abs/2512.24239 |