Degenerate Classical Field Theories and Boundary Theories

Abstract

We introduce a framework for degenerate classical field theories in the BV formalism, which allows us to discuss many interesting examples of theories which do not admit a Lagrangian description. Further, we study phase spaces and boundary conditions for classical field theories on manifolds with boundary, and from a fixed classical field theory together with a choice of boundary condition, construct a degenerate classical field theory on the boundary. We apply these ideas to many physically interesting examples including the Kapustin-Witten twists of N=4 supersymmetric Yang-Mills, Chern-Simons theory, the chiral Wess-Zumino-Witten model, chiral Toda theory, and a new 3d classical field theory called Whittaker theory.

38 pages, content still being updated; comments welcome!

References in corpus (3)

• Supersymmetric gauge theory and the Yangian
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• Quantization of open-closed BCOV theory, I

Cited by in corpus (7)

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• Factorization Algebras for Bulk-Boundary Systems
• Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
• Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications
• Holomorphic boundary conditions for topological field theories via branes in twisted supergravity
• Factorization Algebras for Classical Bulk-Boundary Systems
• Quantizing Derived Mapping Stacks