https://inspirehep.net/files/e1b6c51ad462e854ba7d4bc5853c9171

Grand unified theories and proton decay

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.

https://www.intlpress.com/site/pub/files/_fulltext/journals/cntp/2007/0001/0001/CNTP-2007-0001-0001-a001.pdf

Electric-Magnetic Duality And The Geometric Langlands Program

Aspects of N = 2 supersymmetric gauge theories in three dimensions

These lecture notes are based on the master class given at the Center for the Topology and Quantization of Moduli Spaces, University of Aarhus, August 2007. I provide an introduction to the recent work on the Montonen-Olive duality of N = 4 super-Yang-Mills theory and the Geometric Langlands Program.

http://www.ctqm.au.dk/research/MCS/LectureNotesKapustin.pdf

Lectures on Electric-Magnetic Duality and the Geometric Langlands Program

Fermion number fractionization in quantum field theory

Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

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Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups