Student Colloquium: Kimberly Frey
"Chiral Symmetry Breaking & Bott Periodicity"
Abstract: It was first realized in the early 1960s that non-abelian gauge theories were useful for describing the dynamics of strong interactions. Since then, it has been known that coupling gauge bosons and (massless) fermions results in a rich global symmetry structure, which we refer to as chiral symmetry. However, there exists convincing evidence that the symmetry which appears to be realized by nature is not the full chiral symmetry of the theory—it turns out that chiral symmetry is spontaneously broken due to an attractive interaction between the fermions which effectively causes them to acquire a “mass.” The pattern of symmetry breaking which is observed in nature is related to the specific properties of the mass term which is generated for the fermions, and is only one of many possible patterns which are allowed mathematically. In this talk, I will discuss the results of a recent research project which examined chiral symmetries for (confining) gauge theories in d-dimensional Minkowski space — it turns out that as d changes, both the pattern of chiral symmetry of the theory and the breaking pattern exactly follow the Bott periodicity (which arises in algebraic topology). I will begin by giving an introduction to the general formalism necessary for understanding these results. Following this, I will describe the ways in which chiral symmetry breaking can occur by discussing the possible mass terms for the theory as well as the mass term which, when generated dynamically, yields the largest residual symmetry. In the process, I hope to qualitatively illustrate the intricate interplay between abstract mathematics and modern theoretical physics.
Refreshments will be served prior to the colloquium at 2:30pm in 2214 SES