TL;DR
This paper explores the connection between gauge theory and the geometric Langlands program, focusing on the role of A-branes as eigenbranes under 't Hooft operators, with a review of Higgs bundles and Hitchin fibrations.
Contribution
It provides a direct explanation of why certain A-branes serve as eigenbranes for 't Hooft operators, enhancing understanding of the geometric Langlands correspondence via gauge theory.
Findings
A-branes can act as eigenbranes for 't Hooft operators.
Simplified examples clarify the gauge theory and geometric Langlands link.
Review of Higgs bundles and Hitchin fibrations supports the main argument.
Abstract
The geometric Langlands correspondence was described some years ago in terms of -duality of super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an -brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
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