# Anomalies in the Space of Coupling Constants and Their Dynamical Applications II

### Submission summary

 As Contributors: Ho Tat Lam Arxiv Link: https://arxiv.org/abs/1905.13361v3 Date accepted: 2019-11-05 Date submitted: 2019-10-31 Submitted by: Lam, Ho Tat Submitted to: SciPost Physics Discipline: Physics Subject area: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the $\theta$-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study $SU(N)$ and $Sp(N)$ gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the $\theta$-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### Submission & Refereeing History

Resubmission 1905.13361v3 on 31 October 2019
Submission 1905.13361v2 on 12 September 2019