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

We study the large-N scaling behavior of the theta dependence of the ground-state energy density E(theta) of four-dimensional (4D) SU(N) gauge theories and two-dimensional (2D) CPN-1 models, where theta is the parameter associated with the Lagrangian topological term. We consider its. expansion around theta = 0, E(theta) - E(0) = 1/2 chi theta(2) (1 + b(2)theta(2) + b(4)theta(4) + ...), where chi is the topological susceptibility and b(2n) are dimensionless coefficients. We focus on the first few coefficients b(2n), which parametrize the deviation from a simple Gaussian distribution of the topological charge at theta = 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 theta term. The results provide a robust evidence of the large-N behavior predicted by standard large-N scaling arguments, i.e. b(2n) = O(N-2n). In particular, we obtain b(2) = (b) over bar (2)/N-2 + O(1/N-4) with (b) over bar (2) = -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 theta dependence around theta = 0.