Chiral rings, anomalies and loop equations in Script N = 1* gauge theories

We examine the equivalence between the Konishi anomaly equations and thematrix model loop equations in N=1* gauge theories, the mass deformation of N=4supersymmetric Yang-Mills. We perform the superfunctional integral of twoadjoint chiral superfields to obtain an effective N=1 theory of the thirdadjoint chiral superfield. By choosing an appropriate holomorphic variation,the Konishi anomaly equations correctly reproduce the loop equations in thecorresponding three-matrix model. We write down the field theory loop equationsexplicitly by using a noncommutative product of resolvents peculiar to N=1*theories. The field theory resolvents are identified with those in the matrixmodel in the same manner as for the generic N=1 gauge theories. We cover allthe classical gauge groups. In SO/Sp cases, both the one-loop holomorphicpotential and the Konishi anomaly term involve twisting of index loops tochange a one-loop oriented diagram to an unoriented diagram. The field theoryloop equations for these cases show certain inhomogeneous terms suggesting thematrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and conclusions, 4 references are added, version to appear in JHE