SL(2,C) Chern-Simons theory, flat connections, and four-dimensional quantum geometry

Haggard HM, Han M, Kaminski W, Riello A (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Advances in Theoretical and Mathematical Physics International Press

Book Volume: 23

Pages Range: 1067-1158

Journal Issue: 4

DOI: 10.4310/atmp.2019.v23.n4.a3

Abstract

A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2, C) Chern-Simons theory. The resulting quantum geometrical states are hence represented by the 3d blocks of analytically continued Chern-Simons theory. In the semiclassical limit of this quantization the three-dimensional Chern-Simons action, remarkably, becomes the discrete Einstein-Hilbert action of a 4-simplex, featuring the appropriate boundary terms as well as the essential cosmological term proportional to the simplex's curved 4-volume. Both signs of the curvature and associated cosmological constant are present in the class of flat connections that give rise to this correspondence. We provide a Wilson graph operator that picks out this class of connections. We discuss how to promote these results to a model of Lorentzian covariant quantum gravity encompassing both signs of the cosmological constant. This paper presents the details for the results reported in [1].

Authors with CRIS profile

Muxin Han Chair for Theoretical Physics III (Quantum Gravity)

Involved external institutions

Bard College US United States (USA) (US) University of Warsaw / Uniwersytet Warszawski PL Poland (PL) Perimeter Institute for Theoretical Physics CA Canada (CA)

How to cite

APA:

Haggard, H.M., Han, M., Kaminski, W., & Riello, A. (2019). SL(2,C) Chern-Simons theory, flat connections, and four-dimensional quantum geometry. Advances in Theoretical and Mathematical Physics, 23(4), 1067-1158. https://dx.doi.org/10.4310/atmp.2019.v23.n4.a3

MLA:

Haggard, Hal M., et al. "SL(2,C) Chern-Simons theory, flat connections, and four-dimensional quantum geometry." Advances in Theoretical and Mathematical Physics 23.4 (2019): 1067-1158.

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