Non-perturbative analysis of gauge theories using supergravities

ADS/CFT对应是关于反de Sitter(ADS)时空上的超弦理论或超引力理论与一维低时空上的共形场论(CFT)之间的等价性的猜想。作为研究场论非微扰性质的一种新方法，它引起了人们极大的关注。首先，主要针对具有共形对称性和高度超对称性的理论研究ADS/CFT对应。然而，为了将它应用到更现实的规范理论中，我们必须将其推广到对称性较低的情况。在我们的项目中，我们研究了对称性破缺，以便研究对称性较低的理论的ADS/CFT对应。具体地说，我们使用了六维的最大扩展超引力，它是通过环面紧凑从IIB型超弦获得的。这个六维理论有一个三维ADS时空与一个三维球的直积的解，它对应于具有N=(4，4)超保角对称的二维CFT。我们研究了N=(4，4)超共形对称性是如何通过在CFT侧和超重力侧向量场的微扰来破缺的。这种微扰对应于CFT侧的某些共形权(2，2)或(1，1)算子。我们发现，对于(2，2)微扰，未破缺的对称性是N=(4，2)Poincare超对称，而对于(1，1)微扰，无论是在CFT面还是超引力面，都是N=(4，0)超共形对称性。CFT侧和超重力侧对称性的一致性可以被视为支持ADS/CFT对应猜想的新证据。在此基础上，我们还利用ADS/CFT对应研究了有限温度和有限粒子密度下规范理论的相结构。这项工作仍在调查中。

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.