Free energy and theta dependence of SU(N) gauge theories
  We study the dependence of the free energy on the CP violating angle theta, in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit.   Using the Wilson lattice formulation for numerical simulations, we compute the first few terms of the expansion of the ground-state energy F(theta) around theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta < pi.   We verify that the topological susceptibility has a nonzero large-N limit chi_infinity = 2A with corrections of O(1/N^2), in substantial agreement with the Witten-Veneziano formula which relates chi_infinity to the eta' mass. Furthermore, higher order terms in theta are suppressed; in particular, the O(theta^4) term b_2 (related to the eta' - eta' elastic scattering amplitude) turns out to be quite small: b_2 = -0.023(7) for N=3, and its absolute value decreases with increasing N, consistently with the expectation b_2 = O(1/N^2). 
L. Del Debbio (1), H. Panagopoulos (2), E. Vicari (1) ((1) University   of Pisa and INFN, Pisa, Italy, (2) University of Cyp...