关于AdS/CFT Correspondence中的一个解-红问题
A Comment on the Infra-Red Problem in the AdS/CFT Correspondence
摘要：
本文报道了用严格定义的欧几里德路径积分证明量子场AdS/CFT对应的一些最新进展。我们还对AdS/CFT对应中的红外问题作了评述，并指出它不同于通常的构造性量子场论中的红外问题。为了说明这一点，一个平凡的证明基于超压缩估计的情况下，紫外正则化的潜力类型$:ϕ^4:$。我们还简要讨论了可能的重整化策略和在这种情况下出现的具体问题。
英文摘要：
In this note we report on some recent progress in proving the AdS/CFT correspondence for quantum fields using rigorously defined Euclidean path integrals. We also comment on the infra-red problem in the AdS/CFT correspondence and argue that it is different from the usual IR problem in constructive quantum field theory. To illustrate this, a triviality proof based on hypercontractivity estimates is given for the case of an ultra-violet regularized potential of type $:ϕ^4:$. We also give a brief discussion on possible renormalization strategies and the specific problems that arise in this context.
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