Date of this Version
Proceedings of the Salt Lake City Meeting
This talk describes some work done jointly with L. Alvarez-Gaume, J.B. Bost, G. Moore, and C. Vafa , building on  and [4).
We were concerned with establishing bosonization results on two-dimensional surfaces with complicated topology. Far from being a mere curiosity, bosonization is of great interest in string theory. For example, bosonization has been used in light-cone gauge to prove the equivalence of the Green-Schwarz and NSR superstring . Bosonization also plays a key role in understanding the gauge and super-symmetry of the heterotic string  and in formulating the covariant fermion emission vertex .
The papers ,  generalize existing results on Fermi-Bose equivalence for Fermi fields of any spin on the sphere -. In this talk I will only discuss a subproblem, that of bosonizing spin 1/2 on the torus. It turns out that this problem is only slightly more difficult than the sphere case. One needs a way to "tell" the bosonic theory which of the various spin structures it is to mimic; this is accomplished by adding to the bosonic action a new global term. The new term is already familiar to mathematicians as the parity of a spin structure; it has an immediate generalization to any genus surface.
Electronic version of an article published as [Proceedings of the Salt Lake City Meeting, 1-9 © [copyright World Scientific Publishing Company]
Nelson, P. C. (1987). A New Topological Term in 2d Field Theory. Proceedings of the Salt Lake City Meeting, 396-404. Retrieved from https://repository.upenn.edu/physics_papers/560
Date Posted: 01 May 2017