Abstract Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian -matrix continues to a Kleinian -vector which in turn may be represented by a Poincaré-invariant vacuum state in the Hilbert space built on . contains all information about in a novel, repackaged form. We give an explicit construction of in a Lorentz/conformal basis for a free massless scalar. separates into two halves which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. is shown to be a maximally entangled state in the product of the Hilbert spaces.
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Quantum group intertwiner space from quantum curved tetrahedron
Abstract In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in Haggardet al(2016Ann. Henri Poincaré172001–48). Our method is based on the relation between this phase space and the moduli space of SU(2) flat connections on a 4-punctured sphere. The quantization results in the physical Hilbert space as the solution of the quantum closure constraint, which quantizes the classical closure condition , , for the homogeneously curved tetrahedron. The quantum group emerges as the gauge symmetry of a quantum tetrahedron. The physical Hilbert space of the quantum tetrahedron coincides with the Hilbert space of 4-valent intertwiners of . In addition, we define the area operators quantizing the face areas of the tetrahedron and compute the spectrum. The resulting spectrum is consistent with the usual Loop-Quantum-Gravity area spectrum in the large spin regime but is different for small spins. This work closely relates to 3+1 dimensional Loop Quantum Gravity in presence of cosmological constant and provides a justification for the emergence of quantum group in the theory.
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- Award ID(s):
- 2110234
- PAR ID:
- 10524992
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Classical and Quantum Gravity
- Volume:
- 41
- Issue:
- 16
- ISSN:
- 0264-9381
- Format(s):
- Medium: X Size: Article No. 165008
- Size(s):
- Article No. 165008
- Sponsoring Org:
- National Science Foundation
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