Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice
Abstract
The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.
Versions
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BibTeX
@misc{palumbo2026larger,
title = {{Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice}},
author = {Fabrizio Palumbo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28168},
eprint = {2609.28168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice
AU - Fabrizio Palumbo
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28168
UR - https://arxiv.org/abs/2609.28168
AB - The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.
ER -