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arXiv 2008.01198hep-th
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在AdS ${}_3$中处理散装字段

Dressing bulk fields in AdS${}_3$

Daniel Kabat, Gilad Lifschytz

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摘要：

我们研究了一组CFT运营商适用于重建的带电体标量场$ϕ$在AdS ${}_3$（对偶运营商${\cal O}$的尺寸$Δ$在CFT）在CFT中的存在下，一个保守的自旋$n$电流。我们必须对一堆模糊的非原色标量$\partial_{+}^{m} J^{(m)}$求和，其中$J^{(m)}$是由${\cal O}$和电流构成的扭曲$Δ$和自旋$m$的原色。这些算子的系数可以通过要求体积因子定义良好来确定：通过一个简单的计算，这个要求允许我们直接从CFT计算体积因子。它们是从运动学不变量的特定多项式建立起来的，可以自由地进行场的重新定义。为了订购$1/N$，该程序通过径向广义威尔逊线捕获体标量场的修整。

英文摘要：

We study a set of CFT operators suitable for reconstructing a charged bulk scalar field $ϕ$ in AdS${}_3$ (dual to an operator ${\cal O}$ of dimension $Δ$ in the CFT) in the presence of a conserved spin-$n$ current in the CFT. One has to sum a tower of smeared non-primary scalars $\partial_{+}^{m} J^{(m)}$, where $J^{(m)}$ are primaries with twist $Δ$ and spin $m$ built from ${\cal O}$ and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order $1/N$ this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.

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