Non-perturbative analysis of gauge theories using supergravities

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The AdS/CFT correspondence is a conjecture on equivalence between a superstring theory or a supergravity theory on anti de Sitter(AdS) spacetime and a conformal field theory(CFT) on one-dimensionally lower spacetime. It has attracted a considerable attention as a new method to study non-perturbative properties of field theories. At first the AdS/CFT correspondence was studied mainly for theories which have conformal symmetry and high supersymmetry. To apply it to more realistic gauge theories, however, one has to generalize it to cases with lower symmetries.In our project we have examined symmetry breaking by perturbations in order to study the AdS/CFT correspondence for theories with lower symmetries. Specifically, we have used a maximally extended supergravity in six dimensions, which is obtained from the type IIB superstring by a torus compactification. This six-dimensional theory has a solution of a direct product of three-dimensional AdS spacetime and a three-sphere, which corresponds to a two-dimensional CFT with the N=(4,4) superconformal symmetry. We studied how the N=(4,4) superconformal symmetry is broken by adding a perturbation of vector fields to this solution both in the CFT side and the supergravity side. This perturbation corresponds to certain operators of conformal weight (2,2) or (1,1) in the CFT side. We found that the unbroken symmetry is the N=(4,2) Poincare supersymmetry for the (2,2) perturbation, while it is the N=(4,0) superconformal symmetry for the (1,1) perturbation in both of the CFT side and the supergravity side. The agreement of the unbroken symmetry in the CFT side and the supergravity side may be regarded as new evidence in support of the AdS/CFT correspondence conjecture.After the above work we have also been studying phase structure of gauge theories at finite temperature and finite particle density by applying the AdS/CFT correspondence. This work is still under investigation.