### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 003, 9 pages      arXiv:2210.17512      https://doi.org/10.3842/SIGMA.2023.003
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

### A Note on Coupled Dirac Operators

Nigel J. Hitchin
Mathematical Institute, Woodstock Road, Oxford OX2 6GG, UK

Received November 01, 2022, in final form January 10, 2023; Published online January 13, 2023

Abstract
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.

Key words: Dirac equation; spinor; Yang-Mills; holomorphic structure; index theorem.

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