Free energy and θ dependence of SU(N) gauge theories

✍ Scribed by L. Del Debbio; H. Panagopoulos; E. Vicari

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 258 KB
• Volume: 119
• Category: Article
• ISSN: 0920-5632
• DOI: 10.1016/s0920-5632(03)01657-8

✦ Synopsis

We study the dependence of the free energy on the CP violating angle 19, in four-dimensional SU(iY) gauge theories with N 2 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(0) around 0 = 0, F(B) -F(0) = A202(1 + bzf3' + . ..). Our results support Witten's conjecture: F(B) -F(0) = A@ + 0(1/N) for 0 < T. We verify that the topological susceptibility has a nonzero large-N limit X~ = 2A with corrections of 0(1/N'), in substantial agreement with the Witten-Veneziano formula which relates x0; to the 7' mass. Furthermore, higher order terms in 0 are suppressed; in particular, the 0(19") term bz (related to the rl' -7j elastic scattering amplitude) turns out to be quite small: bl = -0.023(7) for N = 3: and its absolute value decreases wit,h increasing N, consistently with the expectation bZ = 0(1/N').