Theta dependence of SU(N) gauge theories

الأصل · EN

We study the θ dependence of four-dimensional SU(N) gauge theories, for N≥ 3 and in the large-N limit. We use numerical simulations of the Wilson lattice formulation of gauge theories to compute the first few terms of the expansion of the ground-state energy F(θ) around θ=0, F(θ)-F(0) = A₂ θ² (1 + b₂ θ² +...). Our results support Witten's conjecture: F(θ)-F(0) = A θ² + O(1/N) for sufficiently small values of θ, θ< π. Indeed we verify that the topological susceptibility has a nonzero large-N limit χ∞=2 A with corrections of O(1/N²), in substantial agreement with the Witten-Veneziano formula which relates χ∞ to the η′ mass. Furthermore, higher order terms in θ are suppressed; in particular, the O(θ⁴) term b₂ (related to the η′ - η′ elastic scattering amplitude) turns out to be quite small: b₂=-0.023(7) for N=3, and its absolute value decreases with increasing N, consistently with the expectation b₂=O(1/N²).