Non-perturbatively gauge-fixed compact $U(1)$ lattice gauge theory

Abstract

An extensive study of the compact $U(1)$ lattice gauge theory with a higher derivative gauge-fixing term and a suitable counter-term has been undertaken to determine the nature of the possible continuum limits for a wide range of the parameters, especially at strong gauge couplings ($g>1$), adding to our previous study at a single gauge coupling $g=1.3$ \cite{DeSarkar2016}. Our major conclusion is that a continuum limit of free massless photons (with the redundant pure gauge degrees of freedom decoupled) is achieved at any gauge coupling, not necessarily small, provided the coefficient $\tilde{\kappa }$ of the gauge-fixing term is sufficiently large. In fact, the region of continuous phase transition leading to the above physics in the strong gauge coupling region is found to be analytically connected to the point $g=0$ and $\tilde{\kappa }\to \infty$ where the classical action has a global unique minimum, around which weak coupling perturbation theory in bare parameters is defined, controlling the physics of the whole region. A second major conclusion is that, local algorithms like Multihit Metropolis fail to produce faithful field configurations with large values of the coefficient $\tilde{\kappa }$ of the higher derivative gauge-fixing term and at large lattice volumes. A global algorithm like Hybrid Monte Carlo, although at times slow to move out of metastabilities, generally is able to produce faithful configurations and has been used extensively in the current study.

arXiv comment25 pages, 18 figures, version accepted for publication in JHEP

References in corpus (18)

• Abelian chiral gauge theories on the lattice with exact gauge invariance
• A numerical study of confinement in compact QED
• Compact QED under scrutiny: it's first order
• A Gauge-Fixing Action for Lattice Gauge Theories
• Electromagnetic fluxes, monopoles, and the order of the 4d compact U(1) phase transition
• SU(N) chiral gauge theories on the lattice
• Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory
• The Standard Model from a New Phase Transition on the Lattice
• Lattice Chiral Fermions Through Gauge Fixing
• Lattice Gauge Fixing, Gribov Copies and BRST Symmetry
• Chiral Gauge Theory on Lattice with Domain Wall Fermions
• On the Phase Diagram of a Lattice U(1) Gauge Theory with Gauge Fixing
• Manipulating a single adsorbed DNA for a critical endpoint
• Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory
• The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory
• Gauge fixed domain wall fermions on lattice at small Yukawa coupling
• On the continuum limit of gauge-fixed compact U(1) lattice gauge theory
• Tricritical points in a compact $U(1)$ lattice gauge theory at strong coupling

Cited by in corpus (1)

• Photon operators for lattice gauge theory