The super-potential and holomorphic properties of the MQCD Original Research Article

We study the holomorphic properties of the MQCD by comparing the super-potentials in MQCD and the gauge theory. First we show that the super-potential defined as an integral of three form is not appropriate for generic situation with quarks. We report a resolution of the problem which works for the brane configurations of 90 degree rotation, including the true SQCD. The new definition does not need an auxiliary surface and can be reduced to a contour integral for some cases. We find a relation between the new and old definitions, which is verified by explicit calculation for SU(N), SO(N), Sp(N) simple groups with F of massive quarks,