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arXiv 2403.07079hep-th
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带$U(1)$荷的全息与Regge相

Holography and Regge Phases with $U(1)$ Charge

Giulia Fardelli, A. Liam Fitzpatrick, Wei Li

AI总结:

本研究利用全息方法研究d>2维CFT中带U(1)荷低能态的大自旋能谱,分析Q>2时的全息描述,数值对角化哈密顿量并探讨普适性,与3维O(2)模型共形自举结果吻合良好。

摘要:

我们利用全息方法研究了d>2维共形场论(CFT)中,在U(1)守恒流作用下带电荷Q的低能态能谱的大自旋J极限,重点关注d=3和d=4的情形。当Q=2时,这类态的能谱具有普适性,且能被全息理论的长程极限准确描述,无论该CFT本身是否具有全息性质。我们通过考虑AdS体中单光子和引力子交换对Q个标量粒子能量的贡献,详细研究了Q>2时这类态的全息描述;在部分情形中还纳入了标量交换和体接触项。对于一系列有限的Q和J取值,我们对这类态的哈密顿量进行了数值对角化,考察了所得能谱和波函数作为单位荷算符的维度Δ、应力张量与U(1)流的中心荷$c_{\u0001}, c_{\u0002}$的函数关系,发现参数空间中存在多个行为定性不同的区域。我们讨论了将这些结果推广到参数意义上大电荷Q的情形,以及这些结果在超出全息CFT极限下的普适适用程度。我们将全息计算结果与3维O(2)模型在Q=3和Q=4时的共形自举结果进行了对比,发现二者高度吻合。

英文摘要:

We use holography to study the large spin $J$ limit of the spectrum of low energy states with charge $Q$ under a $U(1)$ conserved current in CFTs in $d>2$ dimensions, with a focus on $d=3$ and $d=4$. For $Q=2$, the spectrum of such states is known to be universal and properly captured by the long-distance limit of holographic theories, regardless of whether the CFT itself is holographic. We study in detail the holographic description of such states at $Q>2$, by considering the contribution to the energies of $Q$ scalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values of $Q$ and $J$, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension $Δ$ of the charge-one operator and the central charges $c_{\mathcal{T}}, c_{\mathcal{J}}$ of the stress tensor and U(1) current, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large charge $Q$, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the $3d$ O(2) model at $Q=3$ and $Q=4$ and find excellent agreement.

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