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arXiv 2302.00852hep-th
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德西特与欧几里得反德西特空间中高阶自旋引力的四次局域性

Quartic locality of higher-spin gravity in de Sitter and Euclidean anti-de Sitter space

Yasha Neiman

AI总结:

本文证明(A)dS_4高阶自旋引力在欧几里得边界号差下于大于曲率半径距离处具有局域性,并指出对洛伦兹体时空这意味着德西特空间局域而非反德西特空间。

摘要:

我们考虑(A)dS_4中的高阶自旋引力,其被定义为自由O(N)或Sp(N)矢量模型的全息对偶。在四次阶层面,该理论被认为在大于(A)dS半径的距离上是非局域的,原因在于其边界OPE行为中无质量(twist=1)交换型项的不匹配。我们回顾了这一非局域性论证,并指出它依赖于双光锥极限,而该极限需要洛伦兹边界。在欧几里得OPE极限下,我们通过考察欧几里得AdS中体交换图的已知公式,并构造自旋依赖与位置依赖可因子分解的上界,证明了任意自旋的无质量交换型非局域性均不存在。我们的结果表明,在具有欧几里得边界号差的时空中,高阶自旋理论在大于曲率半径的距离上是局域的。对于洛伦兹体时空,这意味着在德西特空间中具有局域性,而非反德西特空间。

英文摘要:

We consider higher-spin gravity in (A)dS_4, defined as the holographic dual of a free O(N) or Sp(N) vector model. At the quartic level, this theory has been judged non-local at distances greater than the (A)dS radius, due to a mismatch of massless (twist=1) exchange-type terms in its boundary OPE behavior. We review the non-locality argument, and note that it relies on a double-lightcone limit, which requires a Lorentzian boundary. In the Euclidean OPE limit, we demonstrate the absence of massless exchange-type non-localities of any spin, by inspecting a known formula for the bulk exchange diagrams in Euclidean AdS, and constructing upper bounds in which the spin-dependence factorizes from the position-dependence. Our results suggest that higher-spin theory is local (at distances greater than the curvature radius) in spacetimes with Euclidean boundary signature. For Lorentzian bulk, this implies locality in de Sitter space, as opposed to anti-de Sitter.

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