Chern-Simons Origin of Superstring Integrability
Kevin Costello, Bogdan Stefański
Abstract
We derive the AdS_{5}×S^{5} Green-Schwarz superstring from four-dimensional Beltrami-Chern-Simons theory reduced on a manifold with singular boundary conditions. In this construction, the Lax connection and spectral parameter of the integrable superstring have a simple geometric origin in four dimensions as gauge connection and reduction coordinate. κ symmetry arises as a certain class of singular gauge transformations, while the world-sheet metric comes from complex-structure-changing Beltrami differentials. Our approach offers the possibility of investigating integrable holography using traditional field theory methods.
Topics & Concepts
Superstring theoryIntegrable systemConnection (principal bundle)Chern–Simons theoryPhysicsGauge theorySimple (philosophy)Green–Schwarz mechanismTheoretical physicsSymmetry (geometry)Manifold (fluid mechanics)Metric (unit)Field theory (psychology)Field (mathematics)Boundary (topology)Mathematical physicsGauge (firearms)Pure mathematicsSupersymmetryMathematicsQuantum mechanicsMathematical analysisQuantumGeometryQuantum gravityArchaeologyHistoryOperations managementEngineeringEconomicsPhilosophyMechanical engineeringRelationship between string theory and quantum field theoryEpistemologyBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesNoncommutative and Quantum Gravity Theories