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arXiv 1402.7080hep-thgr-qc
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De Sitter空间中局部算子的全息表示

Holographic Representation of Local Operators In De Sitter Space

Xiao Xiao

备注：
35 pages, 3 figures,published in Phys.Rev.D . Comments added, reference fixed
发表信息：
PhysRevD.90.024061(2014)
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摘要：

在dS/CFT对应存在的前提下，通过在未来/过去边界上涂抹共形场论算子，构造了de Sitter空间中的$m^2>\left( \frac{d}{2} \right)^2$局部标量场.为了保持体微观因果关系和恢复体Wightman函数在欧几里德真空中，涂抹处方必须涉及两套单迹运营商的尺寸$Δ$和$d-Δ$。因此，deSitter空间中的局部算子处方不同于反deSitter空间中的解析延拓。在$\mathcal{I}^\pm$中，将全局补丁中的局部算子推到未来/过去无穷远，可以得到共形场论中的单迹算子之间的算子关系，它可以被解释为基变换，也可以被确定为CFT中的算子与其影子算子之间的关系.讨论了自旋$-s$规范场算符的构造，证明了在de Sitter空间中构造高自旋规范场等价于构造具有特定质量参数$m^2<\left( \frac{d}{2} \right)^2$的标量场.构造了一个与边界高自旋流相匹配的非因果高自旋体算符。本文简要介绍了用嵌入形式主义实现AdS和dS中的标量算子构造。

英文摘要：

Assuming the existence of the dS/CFT correspondence, we construct local scalar fields with $m^2>\left( \frac{d}{2} \right)^2$ in de Sitter space by smearing over conformal field theory operators on the future/past boundary. To maintain bulk micro-causality and recover the bulk Wightman function in the Euclidean vacuum, the smearing prescription must involve two sets of single--trace operators with dimensions $Δ$ and $d-Δ$. Thus the local operator prescription in de Sitter space differs from the analytic continuation from the prescription in anti--de Sitter space. Pushing a local operator in the global patch to future/past infinity is shown to lead to an operator relation between single--trace operators in conformal field theories at $\mathcal{I}^\pm$, which can be interpreted as a basis transformation, also identified as the relation between an operator in CFT and its shadow operator. Construction of spin$-s$ gauge field operators is discussed, it is shown that the construction of higher spin gauge fields in de Sitter space is equivalent to constructing scalar fields with specific values of mass parameter $m^2<\left( \frac{d}{2} \right)^2$. An acausal higher spin bulk operator which matches onto boundary higher spin current is constructed. Implementation of the scalar operator constructions in AdS and dS with embedding formalism is briefly described.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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