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Non-perturbative analysis of gauge theories using supergravities

使用超重力对规范理论进行非微扰分析

基本信息

批准号：
15540252
负责人：
TANII Yoshiaki
金额：
$ 0.38万
依托单位：
Saitama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540252/
关键词：
AdS CFT correspondence supergravity conformal field theory supersymmetry 非形場理論

项目摘要

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.

AdS/CFT对应关系是关于反德西特（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）等价性的一个猜想。作为研究场论非微扰性质的一种新方法，它引起了人们的广泛关注。首先对AdS/CFT对应关系进行了研究，主要针对具有保形对称性和高超对称性的理论。然而，为了将它应用于更现实的规范理论，我们必须将它推广到更低对称性的情况。在我们的项目中，为了研究具有较低对称性的理论的AdS/CFT对应，我们检查了扰动的对称破缺。具体地说，我们使用了一个在六维中最大扩展的超引力，它是由IIB型超弦通过环面紧化得到的。该六维理论具有三维AdS时空与三球的直接积的解，对应于具有N=(4,4)超共形对称性的二维CFT。我们研究了N=(4,4)超共形对称是如何通过在CFT侧和超重力侧加入矢量场的扰动而被打破的。这种扰动对应于CFT侧的某些共形权为（2,2）或（1,1）的算子。我们发现（2,2）扰动的不破缺对称性是N=(4,2)庞加莱超对称，而（1,1）扰动在CFT侧和超引力侧都是N=(4,0)超共形对称。CFT侧和超引力侧的不破缺对称性的一致性可以作为支持AdS/CFT对应猜想的新证据。在此基础上，利用AdS/CFT对应关系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。