Strings and discrete fluxes of QCD

We study discrete fluxes in four dimensional SU(N) gauge theories with a mass gap by using brane compactifications which give = 1 or = 0 supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux m is related to the NS two-form modulus B by B = 2π(m/N). These values of B label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of B one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic B does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when B = 2π(m/N). Finally we show that 2π(m/N) behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large N QCD suggesting a T-duality invariance.