skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: The Subelliptic Heat Kernel of the Octonionic Anti-De Sitter Fibration
In this note, we study the sub-Laplacian of the 15-dimensional octonionic anti-de Sitter space which is obtained by lifting with respect to the anti-de Sitter fibration the Laplacian of the octonionic hyperbolic space OH1. We also obtain two integral representations for the corresponding subelliptic heat kernel.  more » « less
Award ID(s):
1901315
PAR ID:
10221352
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Symmetry, Integrability and Geometry: Methods and Applications
ISSN:
1815-0659
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. A<sc>bstract</sc> We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Källén-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Källén-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the Källén-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter. 
    more » « less
  2. A<sc>bstract</sc> We introduce and study a candidate gravity dual to the double scaled SYK model in the form of an exactly soluble 2D de Sitter gravity model consisting of two spacelike Liouville CFTs with complex central charge adding up toc++c= 26. In [1] it was shown that the two-point function of physical operators in a doubled SYK model matches in the semi-classical limit with the Green’s function of a massive scalar field in 3D de Sitter space. As further evidence of the duality, we adapt a result from Zamolodchikov to compute the boundary two-point function of the 2D Liouville-de Sitter gravity model on a disk and find that it reproduces the exact DSSYK two-point function to all orders inλ=p2/N. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity. 
    more » « less
  3. A<sc>bstract</sc> We propose a new model of low dimensional de Sitter holography in the form of a pair of double-scaled SYK models at infinite temperature coupled via an equal energy constraintHL=HR. As a test of the duality, we compute the two-point function between two dressed SYK operators$$ {\mathcal{O}}_{\Delta } $$ O that preserve the constraint. We find that in the largeNlimit, the two-point function precisely matches with the Green’s function of a massive scalar field of mass squaredm2= 4∆(1 – ∆) in a 3D de Sitter space-time with radiusRdS/GN= 4πN/p2. In this correspondence, the SYK time is identified with the proper time difference between the two operators. We introduce a candidate gravity dual of the doubled SYK model given by a JT/de Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter gravity. We comment on the physical meaning of the finite de Sitter temperature and entropy. 
    more » « less
  4. Henneaux, M; Nepomechie, R; Seminara, D (Ed.)
    Abstract In Anti de Sitter space both massive and massless high-spin particles can have consistent local interactions. Both can couple to conserved currents. In this paper we show that when the particles have spin one or greater, there exists a universal feature associated to the particle becoming massive: the currents possess a non-vanishing boundary flux. 
    more » « less
  5. null (Ed.)
    A bstract Force-Free Electrodynamics for black holes in Anti de Sitter is considered. We present new, energy extracting solutions of Force-Free Electrodynamics in Anti de Sitter-Near Horizon Extremal Kerr and Super-Entropic Near Horizon Extremal Kerr geometries. The relevant equations of motion are derived from an action for force-free plasma surrounding spinning black holes with generic asymptotics. We consider the energy flux of electrodynamic fields in rotating frames to argue that the correct measure for energy extraction is the energy flux measured by a rotating observer in the near horizon region. We illustrate this procedure by application to near horizon solutions in Kerr, AdS-Kerr and BTZ. 
    more » « less