On Nonlinear Gauge Theory from a Deformation Theory Perspective

TL;DR

This paper explores the deformation of two-dimensional nonlinear gauge theories based on nonlinear Lie algebras or Poisson algebras, highlighting their uniqueness and potential extensions to higher dimensions.

Contribution

It introduces a novel deformation approach to 2D nonlinear gauge theories and discusses their fundamental uniqueness and possible higher-dimensional generalizations.

Findings

Two-dimensional nonlinear gauge theory is essentially unique.

Deformation quantization relates to correlators on a disk.

Potential extension to higher-dimensional theories.

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.