Supersymmetric theories and nonperturbative effects

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Sakai and collaborators found a new nonperturbative effects by comparing results obtained from supersymmetric gauge theories and nonperturbative effects derived from analysis with branes. They also constructed a series of exact solutions of junctions in linear and nonlinear sigma models with four supercharges. When several lumps coexist in nonlinear sigma models with eight supercharges, they have shown that part of supersymmetry is still preserved if directions of lumps are corelated with the complex structure of the lumps. They also succeeded to construct coexisting solutions for walls and a string. If there are two or more walls of different kind, supersymmetry may be broken completely. They have found a model which admits exact non-BPS solutions of two walls which realize this supersymmetry breaking mechanism. They have shown that topological quantum number makes the configuration stable. These studies help to introduce supersymmetry into models with extra dimensions and to construct soliton solutions such as a stable wail. Tanii and his collaborators mainly studied the AdS/CFT correspondence. In particular, they examined its local symmetry structure and found that local transformations of supergravity in the bulk of anti de Sitter space induce transformations of conformal supergravity on the boundary. Using this result we computed anomalies of a conformal field theory in the conformal supergravity background on the boundary and found that they reproduce the ones obtained by the ordinary field theoretical method. In connection to the AdS/CFT correspondence we studied stability of massive antisymmetric tensor fields with the Chern-Simons type action in anti de Sitter spacetime and found the condition for the stability. We also studied duality symmetries of antisymmetric tensor fields in general even dimensions, and a relation between nonlinear supersymmetry and linear supersymmetry.