arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2412.18366hep-th
收藏

嵌套全息

Nested Holography

Kostas Filippas

备注：
7 pages, 4 figures, 8 appendices; v2: typos corrected, comments added in Epilogue
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文提出一种交换角动量内外自由度的自旋-轨道对偶性，将平坦时空大质量理论全息映射至类光无穷远，并证明其与 AdS/CFT 对偶结合形成嵌套全息桥梁。

摘要：

最近，我们引入了一种关于角动量结构的对称性，它交换了内部和外部自由度。自旋-轨道对偶性是一种全息映射，将四维平坦时空中的大质量理论投影到三维 $\mathbb{S}^2\times\mathbb{R}$ 类光无穷远上。该柱体半径为 $R\sim1/m$，且在量子力学上，其真空态是一个模糊球。研究表明，首先，该对偶性实现了 Hopf 映射，这一事实在超粒子上是明显的。其次，体 Poincarè 群变换为柱体上的共形群。事实上，对偶性的广义版本表明，对偶对称性包括 BMS 群，这正适合类光无穷远。例如，在热力学极限下，$\mathbb{R}^3$ 中的 Landau 能级被证明与对偶 $\mathbb{S}^2$ 上 Dirac 单极子的能级相匹配。该对偶系统实际上被等同于三维临界 Ising 模型。随后，该映射在平坦空间中的 $N_f$ 个大质量费米子上实现，它们确实是柱体上 $2N_f$ 个无质量费米子的全息图。然而，对偶空间实际上是 $\mathbb{S}^2\times\mathbb{R}$ 的共形类，自然包含了共形紧致化 AdS$_4$ 时空的泛覆盖。我们论证了，在无相互作用的情况下，共形边界上的无质量费米子反过来对偶于 AdS$_4$ 中的 $N_f$ 个大质量费米子。对于自由费米子，所有路径积分——$\mathbb{R}^4$、$\mathbb{S}^2\times\mathbb{R}$ 和 AdS$_4$ 中的——都被证明是匹配的。因此，AdS/CFT 对偶性出现在一个更大的背景中，其中一个全息嵌套在另一个全息内部，暗示了平坦空间场与 AdS 超弦之间完整的全息桥梁。

英文摘要：

Recently, we introduced a symmetry on the structure of angular momentum which interchanges internal and external degrees of freedom. The spin-orbit duality is a holographic map that projects a massive theory in four-dimensional flat spacetime onto the three-dimensional $\mathbb{S}^2\times\mathbb{R}$ null infinity. This cylinder has radius $R\sim1/m$ and, quantum-mechanically, its vacuum state is a fuzzy sphere. Progress shows that, first, this duality realizes the Hopf map, a fact manifest on the superparticle. Secondly, the bulk Poincarè group transforms into the conformal group on the cylinder. In fact, the general version of the duality yields that the dual symmetries include the BMS group, as is appropriate at null infinity. As an example, the Landau levels in $\mathbb{R}^3$ are shown to match those of a Dirac monopole on the dual $\mathbb{S}^2$, in the thermodynamic limit. This dual system is actually identified with a three-dimensional critical Ising model. The map is then realized on $N_f$ massive fermions in flat space which, indeed, are the hologram of $2N_f$ massless fermions on the cylinder. However, the dual space is really the conformal class of $\mathbb{S}^2\times\mathbb{R}$, naturally enclosing the universal cover of a conformally compactified AdS$_4$ spacetime. We argue that, in the absence of interactions, the massless fermions on the conformal boundary are in turn dual to $N_f$ massive fermions in AdS$_4$. For free fermions, all path integrals $-$the ones in $\mathbb{R}^4$ and $\mathbb{S}^2\times\mathbb{R}$ and AdS$_4-$ are shown to match. Hence, AdS/CFT duality emerges into a larger context, where one holography nests inside the other, suggesting a complete holographic bridge between fields in flat space and the AdS superstring.

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。

↑