Department of Physics Papers

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Proceedings of the Salt Lake City Meeting

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This talk describes some work done jointly with L. Alvarez-Gaume, J.B. Bost, G. Moore, and C. Vafa [1][2], building on [3] 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 [5][6]. Bosonization also plays a key role in understanding the gauge­ and super-symmetry of the heterotic string [7] and in formulating the covariant fermion emission vertex [8][9].

The papers [1], [2] generalize existing results on Fermi-Bose equivalence for Fermi fields of any spin on the sphere [10]-[13]. 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.

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Electronic version of an article published as [Proceedings of the Salt Lake City Meeting, 1-9 © [copyright World Scientific Publishing Company]


At the time of publication, author Philip C. Nelson was affiliated with Harvard University. Currently, he is a faculty member in the Physics & Astronomy Department at the University of Pennsylvania.

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Date Posted: 01 May 2017