Unification of integrability in supersymmetric gauge theories
Kevin Costello, Junya Yagi
Abstract
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six dimensions, topologically twisted and subjected to an \Omega-deformation. By realizing the six-dimensional theory in string theory and applying dualities, we unify various phenomena in which the eight-vertex model and the XYZ spin chain, as well as variants thereof, emerge from supersymmetric gauge theories.
Topics & Concepts
Gauge theoryPhysicsString theoryIntegrable systemTheoretical physicsUnificationSupersymmetric gauge theoryUnified field theoryOrbifoldSupersymmetryLattice (music)Compactification (mathematics)Hamiltonian lattice gauge theoryString (physics)Mathematical physicsYang–Mills theoryGauge (firearms)S-dualityRelationship between string theory and quantum field theorySuperchargeString field theoryLattice gauge theoryM-theoryQuantum gauge theoryN = 4 supersymmetric Yang–Mills theoryWilson loopIntroduction to gauge theoryLattice field theoryField theory (psychology)Toda latticeF-theoryTopological string theoryParticle physicsQuantum field theoryBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle InteractionsTopological Materials and Phenomena