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 \thetaθ-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)SU(N) and Sp(N)Sp(N) gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \thetaθ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.
Highlights
Measuring the transformation properties of Wilson lines under the center of SUpN q [1].5. This symmetry is intimately connected with confinement: in a deconfined phase it is spontaneously broken, in a confined phase it is preserved [1]
The focus of the previous analysis is on subtle aspects of T symmetry, while in the anomaly in the space of parameters (1.4) T plays no role. This means that the anomaly in the space of parameters, and our resulting dynamical conclusions, persists under T-violating deformations
If the parameter variation is smooth, i.e. it takes place over a distance scale longer than the UV cutoff, the resulting interface dynamics is completely determined by the UV theory
Summary
’t Hooft anomalies are powerful tools for analyzing strongly coupled quantum field theories (QFTs). They constrain the long-distance dynamics and control the properties of boundaries and interfaces, as well as extended excitations like strings and domain walls. [9].) These generalized anomalies of d-dimensional theories can be summarized in terms of classical theories in pd 1q-dimensions but the anomaly action ω depends non-trivially on the coupling constants viewed as background scalar fields varying over spacetime. If the lowenergy theory is nontrivial, i.e. gapless or gapped and topological, it should have the same anomaly If it is gapped and trivial, there must be a phase transition for some value of the parameters..
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