Hughes, Ciaran, 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 |
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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: | 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 |
Related URLs: | |
URI: | https://mu.eprints-hosting.org/id/eprint/5943 |
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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