Strings and discrete fluxes of QCD

We study discrete fluxes in four dimensional SU(N) gauge theories with a ma ss gap by using brane compactifications which give N = 1 or N = 0 supersymm etry. 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 = 2 pi m/N. These values of B label degenerate brane vacua, giving a simple d emonstration of magnetic screening. Furthermore, for these values of B one has a conventional gauge theory on a commutative torus, without having to p erform 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-Klei n modes which must be integrated out to give a four dimensional theory deco uple only when B = 2 pi m/N. Finally we show that 2 pi m/N behaves like a t wo form modulus of the QCD string. This confirms a previous conjecture base d on properties of large N QCD suggesting a T-duality invariance.