Anomalies in the space of coupling constants and their dynamical applications I

• DOI: 10.21468/scipostphys.8.1.001
• Publication Date: 2020-01-06T08:06:13Z
• Authors: Clay Cordova; Daniel Freed; Ho Tat Lam; Nathan Seiberg
• Keywords: Mixed anomaly; Anomaly (physics); Coupling constant

It is customary to couple a quantum system external classical fields. One application the global symmetries of (including Poincaré symmetry) background gauge fields (and metric for symmetry). Failure invariance partition function under transformations these reflects ’t Hooft anomalies. also common view ordinary (scalar) coupling constants as fields, i.e. study theory when they are spacetime dependent. We will show that notion anomalies can be extended naturally include scalar Just allow us deduce dynamical consequences about phases and its defects, same true generalized Specifically, since vary, we learn certain phase transitions must present. demonstrate their applications in simple pedagogical examples one dimension (quantum mechanics) some two, three, four-dimensional field theories. An anomaly an example invertible theory, which described object (generalized) differential cohomology. give introduction this perspective. Also, use Quillen’s superconnections derive free spinor with variable mass. In companion paper theories showing how our unifies extends many recently obtained results.