Rigorous quantization of the nonlinear sigma model on general targets

Develop a satisfactory, rigorous quantization of the nonlinear 2D sigma model on a general target manifold X—beyond special cases such as X=ℝ^n—consistent with the Euclidean field-theoretic structures described in the paper.

Background

The nonlinear sigma model is central to the physics motivation behind the TMF–field theory conjecture. While special cases are tractable, a general, rigorous quantization remains elusive.

The authors state that except for special targets, quantization has not been satisfactorily defined, underlining a foundational gap directly tied to constructing and verifying the desired field-theoretic cocycles.