Hughes, Ciaran and Mehta, Dhagash and Skullerud, Jon-Ivar (2013) Enumerating Gribov copies on the lattice. Annals of Physics, 331. pp. 188-215. ISSN 0003-4916

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Abstract

In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional, it usually has many solutions called Gribov copies. The dependence of the number of Gribov copies, n[U] on the different gauge orbits plays an important role in constructing the Faddeev–Popov procedure and hence in realising the BRST symmetry on the lattice. Here, we initiate a study of counting n[U] for different orbits using three complimentary methods: 1. analytical results in lower dimen- sions, and some lower bounds on n[U] in higher dimensions, 2. the numerical polynomial homotopy continuation method, which numerically finds all Gribov copies for a given orbit for small lattices, and 3. numerical minimisation (“brute force”), which finds many dis- tinct Gribov copies, but not necessarily all. Because n for the coset SU(Nc)/U(1) of an SU(Nc) theory is orbit-independent, we concentrate on the residual compact U(1) case in this article and establish that n is orbit-dependent for the minimal lattice Landau gauge and orbit-independent for the absolute lattice Landau gauge. We also observe that contrary to a previous claim, n is not exponentially suppressed for the recently proposed stereographic lattice Landau gauge compared to the naive gauge in more than one dimension.

Item Type:	Article
Additional Information:	Preprint version of published article, which is available at doi:10.1016/j.aop.2012.12.011
Keywords:	Gribov copies; lattice; gauge fixing;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	5943
Identification Number:	https://doi.org/10.1016/j.aop.2012.12.011
Depositing User:	Dr. Jonivar Skullerud
Date Deposited:	09 Mar 2015 15:40
Journal or Publication Title:	Annals of Physics
Publisher:	Elsevier Masson
Refereed:	Yes
URI:	http://www.journals.elsevier.com/annals-...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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