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

TL;DR

This study investigates the continuum limits of non-perturbatively gauge-fixed compact U(1) lattice gauge theory, showing that free photon behavior emerges at strong couplings with large gauge-fixing terms, and highlights the effectiveness of global algorithms like Hybrid Monte Carlo.

Contribution

It demonstrates that a continuum limit with free massless photons exists at any gauge coupling when the gauge-fixing coefficient is large, extending previous results to strong coupling regimes.

Findings

Continuum limit with free photons achieved at strong coupling with large gauge-fixing term

Global algorithms outperform local algorithms in generating faithful configurations at large gauge-fixing coefficients

The phase transition region connects smoothly to the weak coupling limit at zero gauge coupling

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 $\tilde{\kappa} \rightarrow \infty$ 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.