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arXiv:2509.02173 · The European Physical Journal C

Counting gauge-invariant states with matter fields and finite gauge groups

A. Mariani

Published Nov 17, 2025• 0 citations
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Abstract

Abstract Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we generalize this counting to include the case of scalar and fermionic matter, as well as various kinds of boundary conditions. As a byproduct, we consider several related questions, such as the implementation of charge conjugation for a generic finite group. These results are relevant for resource estimation and also as a crosscheck when working in a gauge-invariant basis.

DOI
10.1140/epjc/s10052-025-15050-8

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We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in any spatial dimension and can be directly applied, among others, to the gauge groups G=U(N)G=U(N)G=U(N) and SU(2N)SU(2N)SU(2N), where $N\ensuremath{\in}\mathbb{N}$. For SU(2N+1)SU(2N+1)SU(2N+1), one can also carry out the transformation after introducing an extra idle Z2{\mathbb{Z}}_{2}Z2​ gauge field, so that the resulting symmetry group trivially contains Z2{\mathbb{Z}}_{2}Z2​ as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.
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