Holographic phenomenology via overlapping degrees of freedom
Abstract
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 anticommuting (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 fieldtheory 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, i.e. using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasiclassical 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 .
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.11016
 arXiv:
 arXiv:2402.11016
 Bibcode:
 2024arXiv240211016F
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 46 pages + appendix