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arXiv 1509.08064hep-thmath-phmath.MP
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维数>2的公理化共形理论与AdS/CT对应

Axiomatic conformal theory in dimensions >2 and AdS/CT correspondence

Albert Schwarz

备注：
15 pages. Minor changes (mostly in terminology)
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摘要：

我们制定公理共形理论（CT）的尺寸$>2$修改西格尔的公理为二维CFT。(In高维CFT的定义还包括能量动量张量存在的条件。我们使用这些公理来推导AdS/CT对应的局部理论AdS。我们引入了弱局域量子场论的概念，并构造了球面$S^d$上的共形理论和$H^{d+1}$上的弱局域量子场论之间的双射对应，它们对于等距是不变的。(Here $H^{d+1}$表示双曲空间=欧几里德AdS空间。）我们用CT关联函数给出了AdS关联函数的表达式。共形理论具有守恒的能量动量张量当且仅当AdS理论在其谱中具有引力子。

英文摘要：

We formulate axioms of conformal theory (CT) in dimensions $>2$ modifying Segal's axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS . We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere $S^d$ and weakly local quantum field theories on $H^{d+1}$ that are invariant with respect to isometries. (Here $H^{d+1}$ denotes hyperbolic space= Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.

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