θ Dependence of the spectrum of SU(N) gauge theories

Abstract

We study the θ dependence of the spectrum of four-dimensional SU(N) gauge theories, where θ is the coefficient of the topological term in the Lagrangian, for N 3 and in the large-N limit. We compute the O(θ2) terms of the expansions around θ ≤ 0 of the string tension and the lowest glueball mass, respectively σ(θ) ≤ σ(1+s2θ2+...) and M(θ) ≤ M(1+g 2θ2+...), where σ and M are the values at θ ≤ 0. For this purpose we use numerical simulations of the Wilson lattice formulation of SU(N) gauge theories for N ≤ 3,4,6. The O(θ2) coefficients turn out to be very small for all N 3. For example, s2 ≤ -0.08(1) and g2 ≤ -0.06(2) for N ≤ 3. Their absolute values decrease with increasing N. Our results are suggestive of a scenario in which the θ dependence in the string and glueball spectrum vanishes in the large-N limit, at least for sufficiently small values of |θ|. They support the general large-N scaling arguments that indicate ≡θ/N as the relevant Lagrangian parameter in the large-N expansion. © SISSA 2006.