Shows that discrete symmetry eliminates the QCD vacuum angle in a hypercubic lattice, suggesting new insights into quantum field theory.
We show that a four-dimensional hypercubic lattice at the Planck scale possesses an exact discrete symmetry that forbids the QCD vacuum angle. The hyperoctahedral group B₄ of the Z⁴ lattice includes independent coordinate reflections under which the topological charge Qₜₒₚ is odd and the gauge action is even. The partition function therefore pairs every field configuration having Qₜₒₚ = +n with one having Qₜₒₚ = -n, forcing θQCD = 0 without axions or new symmetries.
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Mark Newton (2026) studied this question.
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