The spectrum of SU(N) gauge theories at nonzero theta

Details The spectrum of SU(N) gauge theories at nonzero theta The spectrum of SU(N) gauge theories at nonzero theta

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006slft.confe..45p&link_type=abstract

Proceedings of the XXIVth International Symposium on Lattice Field Theory. July 23-28, 2006, Tucson, Arizona., p.45.1

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Scientific paper

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(θ 2 ) terms of the expansions around θ = 0 of the string tension and the lowest glueball mass, respectively σ (θ ) = σ 1 + s2 θ 2 + ... and M(θ ) = M 1 + g2θ 2 + ... , 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(θ 2 ) 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 ≡ θ /N as the relevant Lagrangian parameter in the large-N expansion. ¯

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