On Nonlinear Gauge Theory from a Deformation Theory Perspective

Nonlinear gauge theory is a gauge theory based on a nonlinear Lie algebra (finite W algebra) or a Poisson algebra, which yields a canonical star product for deformation quantization as a correlator on a disk. We pursue nontrivial deformation of topological gauge theory with conjugate scalars in two dimensions. This leads uniquely to a two-dimensional nonlinear gauge theory, which implies its essential uniqueness. We also consider a possible generalization to higher dimensions.