2026/02/28 by H. Alharazin, J. Yu. Panteleeva, B. -D. Sun +1
Physics and Astronomy · #High-Energy Particle Collisions Research #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-ph
paper · pdf · doi:10.1103/n3bh-gs98
openalex publication_date 2026/07/08 · openalex created_date 2026/07/09 · openalex updated_date 2026/07/31
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 parametrization. The model is trained on 10,000 configurations generated via hybrid Monte Carlo at a fixed coupling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>β</a:mi> <a:mn>0</a:mn> </a:msub> <a:mo>=</a:mo> <a:mn>2.0</a:mn> </a:math> on an <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>8</c:mn> <c:mo>×</c:mo> <c:mn>8</c:mn> </c:math> lattice, augmented to 20,000 samples via random gauge transformations. Through physics-conditioned sampling exploiting the linear <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>β</e:mi> </e:math> 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 ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mn>8</g:mn> <g:mo>×</g:mo> <g:mn>8</g:mn> </g:math> ), the model reproduces the exact plaquette with biases <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo stretchy="false">|</i:mo> <i:mi mathvariant="normal">Δ</i:mi> <i:mo stretchy="false">|</i:mo> <i:mo>≤</i:mo> <i:mn>0.001</i:mn> </i:math> for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>β</n:mi> <n:mo>∈</n:mo> <n:mo stretchy="false">[</n:mo> <n:mn>1.5</n:mn> <n:mo>,</n:mo> <n:mn>2.5</n:mn> <n:mo stretchy="false">]</n:mo> </n:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mo stretchy="false">|</r:mo> <r:mi mathvariant="normal">Δ</r:mi> <r:mo stretchy="false">|</r:mo> <r:mo><</r:mo> <r:mn>0.06</r:mn> </r:math> across <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>β</w:mi> <w:mo>∈</w:mo> <w:mo stretchy="false">[</w:mo> <w:mn>1</w:mn> <w:mo>,</w:mo> <w:mn>4</w:mn> <w:mo stretchy="false">]</w:mo> </w:math> . For lattices sharing the training extent <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>L</ab:mi> <ab:mo>=</ab:mo> <ab:mn>8</ab:mn> </ab:math> in at least one direction, biases remain below <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mo>∼</cb:mo> <cb:mn>0.003</cb:mn> </cb:math> for <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>β</eb:mi> <eb:mo>∈</eb:mo> <eb:mo stretchy="false">[</eb:mo> <eb:mn>1.5</eb:mn> <eb:mo>,</eb:mo> <eb:mn>2.5</eb:mn> <eb:mo stretchy="false">]</eb:mo> </eb:math> , 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.