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A new method for analyzing supersymmetric gauge theories is presented. This method relies on the counting of all the chiral operators in the chiral ring of a supersymmetric gauge theory. The counting is done by computing a generating function which counts all possible BPS operators that carry a specified set of global U(1) charges. Remarkably, if the supersymmetric gauge theory lives on N D3 brane in Type IIB string theory, exact results for any number of D3 branes can be written down in a concise and elegant fashion. The paper summarizes results from published work in [1,2,3]. [ABSTRACT FROM AUTHOR]

We study the ADHM construction of instantons in N = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C2/Z2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with spacetime dependent gauge coupling such that the action reproduces the effective action of the fractional branes. [ABSTRACT FROM AUTHOR]

We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on R×S3 as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored. [ABSTRACT FROM AUTHOR]