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Diffusion Models for SU(2) Lattice Gauge Theory in Two Dimensions

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arxiv 2602.09045 v3 pith:DEKCLK3R submitted 2026-02-04 hep-lat hep-ph

Diffusion Models for SU(2) Lattice Gauge Theory in Two Dimensions

classification hep-lat hep-ph
keywords betagaugelatticeconfigurationsdiffusionmodelsbiasescoupling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We apply score-based diffusion models to two-dimensional SU(2) lattice pure gauge theory with the Wilson action, extending recent work on U(1) gauge theories. The SU(2) manifold structure is handled through a quaternion parameterization. The model is trained on 10,000 configurations generated via Hybrid Monte Carlo at a fixed coupling $\beta_0= 2.0$ on an $8\times 8$ lattice, augmented to 20,000 samples via random gauge transformations. Through physics-conditioned sampling exploiting the linear $\beta$-dependence of the score function, we generate configurations at different values of the coupling without retraining; through the fully convolutional U-Net architecture with periodic boundary conditions, we generate configurations on lattices of different spatial extents. We validate our approach by comparing the average plaquette against exact analytical predictions. At the training lattice size ($8\times 8$), the model reproduces the exact plaquette with biases $|\Delta| \leq 0.001$ for $\beta \in [1.5, 2.5]$ and $|\Delta| < 0.06$ across $\beta \in [1, 4]$. For lattices sharing the training extent $L=8$ in at least one direction, biases remain below $\sim 0.003$ for $\beta \in [1.5, 2.5]$, with larger deviations at higher couplings. This work demonstrates that diffusion models are a promising tool for non-Abelian gauge field generation and motivates further investigation toward higher-dimensional theories.

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Cited by 8 Pith papers

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