We analyze the phases of theories having a microscopic 1-form symmetry, starting with a topological 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 and gauge theories in the continuum and on the lattice. Our analysis shows that the generic phases are in , only the confined phase; in , both the confined phase and the topological phase; and in , the confined phase, the topological phase, and a Coulomb phase. We construct a lattice gauge theory with a deformation that, surprisingly, produces up to ( ) 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.
Nguyen, Mendel, et al. "Phases of Theories with <math display='inline'> <mrow> <msub> <mrow> <mi mathvariant='double-struck'>Z</mi> </mrow> <mrow> <mi>N</mi> </mrow> </msub> </mrow> </math> 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles." Physical Review Letters, vol. 134, no. 14, Apr. 2025. https://doi.org/10.1103/PhysRevLett.134.141902
Nguyen, Mendel, Sulejmanpasic, Tin, and Ünsal, Mithat, "Phases of Theories with <math display='inline'> <mrow> <msub> <mrow> <mi mathvariant='double-struck'>Z</mi> </mrow> <mrow> <mi>N</mi> </mrow> </msub> </mrow> </math> 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles," Physical Review Letters 134, no. 14 (2025), https://doi.org/10.1103/PhysRevLett.134.141902
@article{osti_2549436,
author = {Nguyen, Mendel and Sulejmanpasic, Tin and Ünsal, Mithat},
title = {Phases of Theories with <math display='inline'> <mrow> <msub> <mrow> <mi mathvariant='double-struck'>Z</mi> </mrow> <mrow> <mi>N</mi> </mrow> </msub> </mrow> </math> 1-Form Symmetry, and the Roles of Center Vortices and Magnetic Monopoles},
annote = { We analyze the phases of theories having a microscopic Z N 1-form symmetry, starting with a topological 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 phase; and in d = 4 , the confined phase, the topological 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. Published by the American Physical Society 2025 },
doi = {10.1103/PhysRevLett.134.141902},
url = {https://www.osti.gov/biblio/2549436},
journal = {Physical Review Letters},
issn = {ISSN PRLTAO},
number = {14},
volume = {134},
place = {United States},
publisher = {American Physical Society},
year = {2025},
month = {04}}