Anomalies
Seminar Course in the Winter Semester 2026/27
The breakdown of a classical symmetry upon quantization occupies a central role in modern theoretical physics. Once viewed as structural pathologies or mathematical nuisances, anomalies are now understood as powerful non-perturbative tools that constrain renormalization group flows, classify topological phases of matter, and dictate the consistency conditions of string theory.
This seminar aims to chart a journey through the various incarnations of anomalies in modern physics and draw links between seemingly different notions of anomalies appearing throughout the literature.
Time and place
Anticipated time slot is Thursday 2-4pm, first class October 15.
Organizational meeting: Wednesday, July 22, 2026, at 11h c.t. in SR 5
Description
(Preliminary) Plan
- Part I will aim to discuss anomalies in the simplest possible models of 0-dim and 1-dim (QM) quantum systems to avoid analytic features of more complicated instances of anomalies and to really isolate the main cause of the phenomenon.
- Part II aims to cover historical origin of anomalies as well as the original technical tools used to derive them.
- Part III refocuses on applications in string theory . We will discuss things such as Green-Schwarz mechanism, Weyl anomaly and holomorphic anomaly.
- Part IV is about studying the implications of anomalies in condensed matter physics and phycics of quantum phase transitions. As such we can re frame symmetry-protected topological (SPT) phases as invertible topological field theories.
- Part V reaches the modern frontiers of mathematical physics. Modern language of generalized higher-form global symmetries will be introduced to put various perspective discussed thus far on an equal footing.
Prerequisites
A thorough knowledge of Quantum Field Theory will be assumed as well as basic understanding of Representation Theory and Differential Geometry/Topology. Introductory String Theory is advantageous but not strictly mandatory.
Credits and Evaluation
The course is listed as ``Masterseminar'' in both Physics and Mathematics. Evaluation is based on a 60-minute presentation, active participation in discussions, and consistent attendance. The language of instruction is English.
