On Nonlinear Gauge Theory from a Deformation Theory Perspective

Abstract

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 to two-dimensional nonlinear gauge theory exclusively, which implies its essential uniqueness. We also consider a possible extension to higher dimensions.