标题： 通过重叠自由度的全息现象学 显示英文标题

标题： Holographic phenomenology via overlapping degrees of freedom

摘要： 全息原理表明，空间区域中的物理自由度比传统量子场论所暗示的要少。 同时，在大维数的希尔伯特空间$2^n$中，可以定义几乎反对易（但不完全）的$N \gg n$泡利代数，这些可以看作是“重叠的自由度”。 我们提出通过允许场论模式相互重叠来模拟全息理论的现象，并推导出潜在的观测后果。 特别是，我们构建了一个费米子量子场，其有效自由度近似遵循面积缩放并满足宇宙的贝肯斯坦边界，并将该模型的预测与宇宙中微子观测进行比较。 我们对全息性的实现意味着平面波具有有限的寿命，这取决于理论的整体紫外截断。 为了允许来自耀变体 TXS 0506+056 的中微子通量可被观测，我们的模型需要有一个截断$k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$。 这与 IceCube 对宇宙中微子能量谱的当前限制大致一致，但高能中微子对我们全息性模型是一个潜在挑战。 我们通过量子mereology来支持我们的构造，\ie ，使用有效场论自由度应通过寻找准经典希尔伯特空间分解从量子引力的抽象理论中出现的想法。 我们还讨论了如何将该框架扩展到玻色子。 最后，利用随机矩阵理论的结果，我们得出了对理论能量谱的解析理解。 本工作中使用的数值工具在 GPUniverse 包中公开可用，https://github.com/OliverFHD/GPUniverse 。 显示英文摘要

摘要： The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as "overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory. The numerical tools used in this work are publicly available within the GPUniverse package, https://github.com/OliverFHD/GPUniverse .