**Title:** Yang-Mills theory and the large-N limit

**Speaker:** Brian Hall

**Speaker Info:** University of Notre Dame

**Brief Description:**

**Special Note**:

**Abstract:**

Yang-Mills theory is a generalization of Maxwell’s equation for electromagnetic fields. The quantum version of Yang-Mills theory describes the strong nuclear force and is a crucial part of the standard model of particle physics. The theory is typically described by means of a heuristic “path integral” over the space of all fields. Although a rigorous theory in four space-time dimensions remains elusive, the two-dimensional path integral allows for a mathematically rigorous description as a white noise.I will begin by explaining the physical meaning of Yang-Mills fields and then give a mathematical description of the two-dimensional path integral. Finally, I will discuss some recent results about the large-N limit, which arises by taking the “structure group” of the theory to be the unitary group U(N) and taking N to infinity. This limit is related to large-N limit considered in random matrix theory.

The talk will be largely self contained; no prior knowledge of physics will be assumed. Portions of the talk will describe joint work with Bruce Driver, Franck Gabriel, and Todd Kemp.

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