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We test the eigenstate thermalization hypothesis (ETH) for 2+1 dimensionalSU(2) lattice gauge theory. By considering the theory on a chain of plaquettesand truncating basis states for link variables at $j=1/2$, we can map it onto aquantum spin chain with local interactions and numerically exactly diagonalizethe Hamiltonian for reasonably large lattice sizes. We find energy levelrepulsion in momentum sectors with no remaining discrete symmetry. We study twolocal observables made up of Wilson loops and calculate their matrix elementsin the energy eigenbasis, which are shown consistent with the ETH.

SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis