Topological aspects of 4D abelian lattice gauge theories with the \(\theta\) parameter. (English) Zbl 1457.81081
Summary: We study a four-dimensional U(1) gauge theory with the \(\theta\) angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at \(\theta = \pi\), and show how its appearance can be consistent with the anomaly constraint. We also construct the \(\mathrm{SL} (2, \mathbb{Z} )\) self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed ’t Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and ’t Hooft anomaly with those of SU \((N)\) Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-abelian gauge theories with nonzero \(\theta\) angles.
MSC:
| 81T25 | Quantum field theory on lattices |
| 81T45 | Topological field theories in quantum mechanics |
| 81T50 | Anomalies in quantum field theory |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
Keywords:
anomalies in field and string theories; confinement; solitons monopoles and instantons; topological states of matterReferences:
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