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arXiv 2207.05085hep-th
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纯反de Sitter超引力与共形引导

Pure anti-de Sitter supergravity and the conformal bootstrap

Luis F. Alday, Shai M. Chester

摘要:

本文研究了在没有额外紧致时空因子的情况下,在$d=3,4,\text{and $ 6 $}$的$d+1$维下,反德西特空间(AdS)上极大超引力中的引力子散射.全息表明,这个理论是对偶的异国情调的最大超对称共形场论(CFT)在$d$维的唯一轻单迹算子是应力张量。这与更标准的情况形成对比,比如$AdS_5\times S^5$上的IIB型弦理论与$\mathcal{N}=4$ Super-Yang-Mills的对偶,其中CFT对$S^5$上的每个卡鲁扎-克莱因模都有轻的单迹算子。我们计算了纯AdS $_{d+1}$理论在小普朗克长度展开中的1-圈修正,这与CFT中的大中心电荷展开是对偶的。我们发现,这种校正饱和的最一般的非微扰共形自举边界上的相关器在大的中心电荷制度$d=3,4,6$,而1-循环校正与弦/M-理论的CFTs的所有谎言内的允许区域。

英文摘要:

We consider graviton scattering in maximal supergravity on Anti-de Sitter space (AdS) in $d+1$ dimensions for $d=3,4,\text{and $6$}$ with no extra compact spacetime factor. Holography suggests that this theory is dual to an exotic maximally supersymmetric conformal field theory (CFT) in $d$ dimensions whose only light single trace operator is the stress tensor. This contrasts with more standard cases like Type IIB string theory on $AdS_5\times S^5$ dual to $\mathcal{N}=4$ Super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on $S^5$. We compute the 1-loop correction to the pure AdS$_{d+1}$ theory in a small Planck length expansion, which is dual to the large central charge expansion in the CFT. We find that this correction saturates the most general non-perturbative conformal bootstrap bounds on this correlator in the large central charge regime for $d=3,4,6$, while the 1-loop correction to CFTs with string/M-theory duals all lie inside the allowed region.

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