Phases of Theories with Z_{N} 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles.

Authors

Mendel Nguyen, Tin Sulejmanpasic, Mithat Ünsal

Published in

Physical review letters. Volume 134. Issue 14. Pages 141902. Apr 11, 2025.

Abstract

We analyze the phases of theories having a microscopic Z_{N} 1-form symmetry, starting with a topological BF theory and deforming it so that only the microscopic symmetry is preserved. These theories have a well-defined notion of confinement, prototypical examples being pure SU(N) and Z_{N} gauge theories in the continuum and on the lattice. Our analysis shows that the generic phases are in d=2, only the confined phase; in d=3, both the confined phase and the topological BF phase; and in d=4, the confined phase, the topological BF phase, and a Coulomb phase. We construct a Z_{N} lattice gauge theory with a deformation that, surprisingly, produces up to (N-1) photons. We give an interpretation of these findings in terms of the behaviors of two competing drivers of confinement-magnetic monopoles and center vortices-and conclude that proliferation of center vortices is necessary but insufficient for confinement, while proliferation of magnetic monopoles is both necessary and sufficient.

PMID:
40279580
Bibliographic data and abstract were imported from PubMed on 26 Apr 2025.

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