Octonions and Quantum Gravity through the Central Charge Anomaly in the Clifford Algebra

• URL: http://arxiv.org/abs/2304.14830v2
• Date: Mon, 25 Sep 2023 20:43:07 GMT
• Title: Octonions and Quantum Gravity through the Central Charge Anomaly in the Clifford Algebra
• Authors: Lucas Kocia Kovalsky
• Abstract summary: We derive a theory of quantum gravity containing an AdS$_3$ isometry/qubit duality. We extend the theory through supersymmetry- and conformal-breaking $mathcal O(G)$ transformations of the embedding to produce perturbed AdS$_3$ spacetimes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a theory of quantum gravity containing an AdS$_3$ isometry/qubit duality. The theory is based on a superalgebra generalization of the enveloping algebra of the homogeneous AdS$_3$ spacetime isometry group and is isomorphic to the complexified octonion algebra through canonical quantization. Its first three quaternion generators correspond to an $\hbar$-quantized AdS$_3$ embedded spacetime and its remaining four non-quaternion generators to a $G$-quantized embedding $2+2$ Minkowski spacetime. The quaternion algebra's expression after a monomorphism into the complexified Clifford algebra produces a two-dimensional conformal operator product expansion with a central charge anomaly, which results in an area-law $\hbar G$ scaling satisfying the holographic principle and defines an "arrow of time". This relationship allows us to extend the theory through supersymmetry- and conformal-breaking $\mathcal O(G)$ transformations of the embedding to produce perturbed AdS$_3$ spacetimes and derive a resolution to the black hole information paradox with an explicit mechanism.

Related papers

• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• The hidden Lorentz Covariance of Quantum Mechanics [0.552480439325792]
  We show that each mass sector of the Hilbert space carries a representation of the Lorentz algebra, and the (anti) de-Sitter algebra on each mass sector contracts to the Poincare algebra. We also show that three-dimensional fuzzy space also carries a unitary representation of these algebras.
  arXiv  Detail & Related papers  (2023-12-25T15:18:57Z)
• Quantum teleportation in the commuting operator framework [63.69764116066747]
  We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
  arXiv  Detail & Related papers  (2022-08-02T00:20:46Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Asymptotically flat boundary conditions for the $U(1)^3$ model for Euclidean Quantum Gravity [0.0]
  We study boundary conditions and symmetries of the $U(1)3$ model. One finds that exactly the non-Abelian part of the $SU(2)$ Gauss constraint which is absent in the $U(1)3$ model plays a crucial role in obtaining boost and rotation generators.
  arXiv  Detail & Related papers  (2020-10-30T16:31:49Z)
• Trace dynamics and division algebras: towards quantum gravity and unification [0.0]
  We propose a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang-Mills fields, and fermions. We explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. We predict a new massless spin one boson [the Lorentz boson] which should be looked for in experiments.
  arXiv  Detail & Related papers  (2020-09-10T15:37:19Z)
• The Standard Model, The Exceptional Jordan Algebra, and Triality [0.0]
  We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space $(mathbbCotimesmathbbO)2$ of the complex octonionic projective plane.
  arXiv  Detail & Related papers  (2020-06-29T18:00:06Z)
• Conformal bridge between asymptotic freedom and confinement [0.0]
  We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. We investigate the one- and two-dimensional examples that reveal, in particular, a curious relation between the two-dimensional free particle and the Landau problem.
  arXiv  Detail & Related papers  (2019-12-26T02:45:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.