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arXiv · 2512.24239

Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry

Robert Hanson
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Abstract

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.

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Robert Hanson. 2025-12-30. Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry. https://arxiv.org/abs/2512.24239

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