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1 September 2020 The extended Bogomolny equations with generalized Nahm pole boundary conditions, II
Siqi He, Rafe Mazzeo
Duke Math. J. 169(12): 2281-2335 (1 September 2020). DOI: 10.1215/00127094-2020-0009

Abstract

We develop a Kobayashi–Hitchin correspondence for the extended Bogomolny equations, that is, the dimensionally reduced Kapustin–Witten equations, on the product of a compact Riemann surface Σ with R y + , with generalized Nahm pole boundary conditions at y = 0 . The correspondence is between solutions of these equations satisfying these singular boundary conditions and also limiting to flat connections as y and certain holomorphic data consisting of triplets ( E , φ , L ) , where ( E , φ ) is a stable SL ( n + 1 , C ) Higgs pair and L E is a holomorphic line bundle. This corroborates a prediction of Gaiotto and Witten and serves as an extension of our earlier article which treats only the SL ( 2 , R ) case.

Citation

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Siqi He. Rafe Mazzeo. "The extended Bogomolny equations with generalized Nahm pole boundary conditions, II." Duke Math. J. 169 (12) 2281 - 2335, 1 September 2020. https://doi.org/10.1215/00127094-2020-0009

Information

Received: 18 June 2018; Revised: 20 November 2019; Published: 1 September 2020
First available in Project Euclid: 18 June 2020

MathSciNet: MR4139043
Digital Object Identifier: 10.1215/00127094-2020-0009

Subjects:
Primary: 58D27
Secondary: 81T13

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 12 • 1 September 2020
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