Operator anomaly and a 4d analog of the Kac-Moody algebra

by Prof. Anton Kapustin (California Institute of Technology)

Tuesday 24 Sep 2024, 10:10 → 11:10 Asia/Shanghai

S408

Abstract: It is well-known that chiral anomaly of 2d field theories can be phrased as an operator statement. Namely, the algebra of normal-ordered charge densities is centrally extended. In the case of 4d field theories, L. Faddeev argued a long time ago that chiral anomaly causes the algebra of charge densities to be modified by terms which depend on the external gauge field. These terms vanish when the field is set to zero. Faddeev’s proposal is not completely sastifactory because the anomaly is a property of the theory even before gauging. I propose an alternative scenario and check it by a computation in a classical 4d Wess-Zumino-Witten model.

Bio:
Anton Kapustin is currently the Earle C. Anthony Professor of Theoretical Physics at the California Institute of Technology. His interests lie in quantum field theory and string theory, and their applications to particle physics and condensed matter theory.