2024/06/02 by G. E. Volovik, Volovik, G. E.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #Noncommutative and Quantum Gravity Theories #Other Condensed Matter (cond-mat.other)
paper · pdf · doi:10.48550/arxiv.2406.00718
openalex publication_date 2024/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the discrete Z4 symmetry \bf i, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter. Under this symmetry operation \bf i, the emerging tetrads are multiplied by the imaginary unit, \bf i eaμ= - i eaμ. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter 3He-B is the analogue of the tetrad field, but it has complex values. The \bf i-symmetry operation changes the phase of the complex order parameter by π/2, which corresponds to the Z4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z4 symmetry, in which the \bf i-operation changes sign of the scalar curvature, \bf i \cal R = - \cal R, and thus the Einstein-Hilbert action violates the \bf i-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K=1/16πG plays the role of the order parameter, which changes sign under \bf i-transformation.