MS Seminar (Mathematics - String Theory)

Speaker: Aleksey Cherman (Minnesota)
Title: Large N volume independence and bosonization
Date: Tue, Feb 05, 2013, 13:15 - 14:45
Place: Seminar Room A
Related File: 841.pdf
Abstract: Part 1: Thirty years ago, Eguchi and Kawai suggested that large N gauge theories have a remarkable property which came to be known as large N volume independence. When this notion is valid, it has the striking consequence that an interesting class of observables in e.g. gauge theories living on R^3 \times S^1 does not dependent of the size of the S^1 in the large N limit. However, examples of theories for which volume independence is valid were found only very recently, and include certain interesting supersymmetric and non-supersymmetric QCD-like gauge theories. Crucial to the recent advances was the development of the idea of large N orbifold equivalence for field theories, which originated in string theory. The combination of the two ideas leads to large N equivalences between field theories living in a different numbers of spatial dimensions. I will give an overview of the physics behind the intertwined notions of large N volume independence and orbifold equivalences and sketch some applications.

Part2: The notion of bosonization is normally thought of as being particular to 2D field theories, and D>2 field theories with fermions are not expected to have local bosonic descriptions except in very special cases. I will explain how the ideas of large N volume independence and orbifold equivalence can be used to add to this list of special cases. In particular, I will explain a large N equivalence between 3D SU(N) YM theory with N_f adjoint fermions (which is supersymmetric for N_f=1) and a certain 2D gauge theory in the large N limit. A fairly straightforward application of non-Abelian bosonization to the the 2D gauge theory yields a purely bosonic local 2D theory, which at large N will have a class of observables which coincide with those in the original 3D fermionic theory. Hence the bosonized version of the three-dimensional large N gauge theory turns out to live in two dimensions.