θ dependence of 4D SU (N) gauge theories in the large- N limit

We study the large-N scaling behavior of the θ dependence of the ground-state energy density E(θ) of four-dimensional (4D) SU(N) gauge theories and two-dimensional (2D) CPN-1 models, where θ is the parameter associated with the Lagrangian topological term. We consider its θ expansion around θ=0, E(θ)-E(0)=12χθ2(1+b2θ2+b4θ4+...), where χ is the topological susceptibility and b2n are dimensionless coefficients. We focus on the first few coefficients b2n, which parametrize the deviation from a simple Gaussian distribution of the topological charge at θ=0. We present a numerical analysis of Monte Carlo simulations of 4D SU(N) lattice gauge theories for N=3, 4, 6 in the presence of an imaginary θ term. The results provide a robust evidence of the large-N behavior predicted by standard large-N scaling arguments, i.e. b2n=O(N-2n). In particular, we obtain b2=b2/N2+O(1/N4) with b2=-0.23(3). We also show that the large-N scaling scenario applies to 2D CPN-1 models as well, by an analytical computation of the leading large-N θ dependence around θ=0.