Digitization and subduction of $SU(N)$ gauge theories

• URL: http://arxiv.org/abs/2405.12204v2
• Date: Tue, 28 May 2024 17:02:27 GMT
• Title: Digitization and subduction of $SU(N)$ gauge theories
• Authors: Benoît Assi, Henry Lamm,
• Abstract summary: We show that subduction offers valuable information based on subduced direct sums. We compute the static potentials of all irreducible representations of $ Sigma(360 times 3) $ at a fixed lattice spacing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still need to be clarified. To gain insights, we investigate the subduction of $ SU(2) $ and $ SU(3)$ to discrete crystal-like subgroups. Using classical lattice calculations, we show that subduction offers valuable information based on subduced direct sums, helping us identify additional terms to incorporate into the lattice action that can mitigate the effects of digitization. Furthermore, we compute the static potentials of all irreducible representations of $ \Sigma(360 \times 3) $ at a fixed lattice spacing. Our results reveal a percent-level agreement with the Casimir scaling of ( SU(3) ) for irreducible representations that subduce to a single $ \Sigma(360 \times 3) $ irreducible representation. This provides a diagnostic measure of approximation quality, as some irreducible representations closely match the expected results while others exhibit significant deviations.

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