Strings and discrete fluxes of QCD

We study discrete fluxes in brane constructions of QCD-like theories. It is shown that when these theories are compactified on a torus, a periodic potential is generated for the Neveu-Schwarz two-form modulus $B$. The minima of this potential are given by $B = 2\pi m/N$, where $m$ is the 't Hooft flux and $N$ is the rank of the gauge group. The underlying reason for this potential is the existence of a mass gap. In this case one is not allowed a continuous range for $B$ corresponding to non-commutative deformations of the torus. We show that $B$ behaves like the two form modulus of the QCD string, as well as the IIA string. This equivalence has been conjectured previously based on properties of large N QCD suggesting a T-duality invariance. Finally we show that the relation $B = 2\pi m/N$ permits fractional D0-brane charge without violating Dirac quantization in the presence of a D6-brane.