Disorder operators and magnetic vortices in SU(N) lattice gauge theory

Manu Mathur; Atul Rathor

Home/Archive/arXiv

arXiv · 2307.06278

Disorder operators and magnetic vortices in SU(N) lattice gauge theory

Manu Mathur·Atul Rathor

View original source ↗Read source document ↗Export metadata ↓

Abstract

We construct the most general disorder operator for SU(N) lattice gauge theory in $(2+1)$ dimension by using exact duality transformations. These disorder operators, defined on the plaquettes and characterized by ($\text{N}-1$) angles, are the creation \& annihilation or the shift operators for the SU(N) magnetic vortices carrying $(\text{N}-1)$ types of magnetic fluxes. They are dual to the SU(N) Wilson loop order operators which, on the other hand, are the creation-annihilation or shift operators for the $(\text{N}-1)$ electric fluxes on their loops. The new order-disorder algebra involving SU(N) Wigner D matrices is derived and discussed. The $Z_\text{N} (\in $ SU(N)) 't Hooft operator is obtained as a special limit. In this limit we also recover the standard Wilson-'t Hooft order-disorder algebra. The partition function representation and the free energies of these SU(N) magnetic vortices are discussed.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Manu Mathur, Atul Rathor. 2023-07-12. Disorder operators and magnetic vortices in SU(N) lattice gauge theory. https://arxiv.org/abs/2307.06278

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

When the center matters: color screening and gluelumps in dihedral lattice gauge theories

Confinement is one of the hallmarks of quantum chromodynamics (QCD), but its first-principles characterization remains elusive. We show that discrete non-Abelian lattice gauge theories (LGTs) with dihedral groups $D_N$ provide a minimal setup for characterizing the connection between confinement and the group center. When the latter is trivial (odd $N$), gluon clouds screen static charges, forming composite objects known as gluelumps. These are stable excitations of the theory, in contrast to their QCD analog. As a consequence, string breaking can occur through fluctuations of the electric field only, without pair nucleation from the vacuum. Our results showcase how the rich physics typically associated with QCD emerges in much simpler discrete non-Abelian LGTs, making them ideal settings to test this phenomenology both in numerical calculations and in near-term quantum devices.

hep-lat↗

arXiv2026

Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.

hep-lat↗

arXiv2026

Quantum anomaly for benchmarking quantum computing

Given the rapid advances in quantum computing hardware, establishing strategies for verifying the correctness of quantum computations has become increasingly important. Exploiting the fact that the axial anomaly in gauge theories is exact to all orders in perturbation theory, we propose the axial anomaly as a nontrivial benchmark for quantum simulations of lattice gauge theories. We simulate axial charge production in ${\mathbb Z}_N$ lattice gauge theories on the trapped-ion quantum computer ``Reimei''. After taking the U(1), infinitesimal time, and infinite volume limits, we successfully reproduce the anomaly coefficient within statistical uncertainties, even without error mitigation. Our results demonstrate that the axial anomaly can be simulated on current quantum computers and serves as a verification test of quantum computations.

hep-lat↗