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Aspects of Supersymmetric Gauge Theory and String Theory
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In the first part of this thesis we study sometopics in N=1 supersymmeric gauge theory and therelation tomatrix models. We review the relevantnon-perturbative techniquesfor computing effective superpotential, such asSeiberg-Wittencurve. Then we review the proposal of Dijkgraaf andVafa thatrelates the glueball superpotentials to thecomputation in matrixmodels. We then consider a case of multi-tracesuperpotential. Weperform the perturbative computation of glueballsuperpotential inthis case and explain the subtlety in identifying theglueballsuperfield. We also use these techniques to studyphases of N=1gauge theory with flavors. In the second part westudy topics inAdS/CFT correspondence and its plane wave limit. Wereview theplane wave geometry and BMN operators thatcorresponding tostring modes. Then we study string interactions inthe case of ahighly curved plane wave background, and demonstrate theagreements between calculations of string interactionamplitudes inthe two dual theories. Finally we study D3-branegiant gravitonsand open string attached to them. Giant gravitons arenon-perturbative objects that have very large R-charge.
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