Supersymmetric gauge theory and the Yangian

Abstract

This paper develops a new connection between supersymmetric gauge theories and the Yangian. I show that a twisted, deformed version of the pure N=1 supersymmetric gauge theory is controlled by the Yangian, in the same way that Chern-Simons theory is controlled by the quantum group. This result is used to give an exact calculation, in perturbation theory, of the expectation value of a certain net of n+m Wilson operators in the deformed N=1 gauge theory. This expectation value coincides with the partition function of a spin-chain integrable lattice model on an n-by-m doubly-periodic lattice.

145 pages

References in corpus (13)

• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Quantum Groups and Quantum Cohomology
• Another proof of M. Kontsevich formality theorem
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Quantization of Lie bialgebras, V
• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Electric-Magnetic Duality And The Geometric Langlands Program
• The blob complex
• Formality of Chain Operad of Small Squares
• Meromorphic tensor categories
• Yangian Symmetry in N=4 super Yang-Mills
• Derived Higher Hochschild Homology, Topological Chiral Homology and Factorization algebras

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