On gravity unification in SL(2N,C) gauge theories

J. L. Chkareuli

doi:10.1140/epjc/s10052-024-13574-z

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 1212
https://doi.org/10.1140/epjc/s10052-024-13574-z

Regular Article

On gravity unification in SL(2N,C) gauge theories

J. L. Chkareuli¹^,2^a

¹ Institute of Theoretical Physics, Ilia State University, 0162, Tbilisi, Georgia
² Andronikashvili Institute of Physics, Tbilisi State University, 0177, Tbilisi, Georgia

^a j.chkareuli@iliauni.edu.ge

Received: 1 October 2024
Accepted: 5 November 2024
Published online: 22 November 2024

Abstract

The local SL(2N, C) symmetry is shown to provide, when appropriately constrained, a viable framework for a consistent unification of the known elementary forces, including gravity. Such a covariant constraint implies that an actual gauge field multiplet in the SL(2N, C) theory is ultimately determined by the associated tetrad fields which not only specify the geometric features of spacetime but also govern which local internal symmetries are permissible within it. As a consequence, upon the covariant removal of all “redundant” gauge field components, the entire theory only exhibits the effective $S L (2, C) \times S U (N)$ $SL(2,C)\times SU(N)$ symmetry, comprising SL(2, C) gauge gravity on one hand and SU(N) grand unified theory on the other. Given that all states involved in the SL(2N, C) theories are additionally classified according to their spin values, many potential SU(N) GUTs, including the conventional SU(5) theory, appear to be irrelevant for standard spin 1/2 quarks and leptons. Meanwhile, applying the SL(2N, C) symmetry to the model of composite quarks and leptons with constituent chiral preons in its fundamental representations reveals, under certain natural conditions, that among all accompanying $S U {(N)}_{L} \times S U {(N)}_{R}$ $SU(N)_{L}\times SU(N)_{R}$ chiral symmetries of preons and their composites only the $S U {(8)}_{L} \times S U {(8)}_{R}$ $SU(8)_{L}\times SU(8)_{R}$ meets the anomaly matching condition ensuring masslessness of these composites at large distances. This, in turn, identifies SL(16, C) with the effective $S L (2, C) \times S U (8)$ $SL(2,C)\times SU(8)$ symmetry, accommodating all three quark-lepton families, as the most likely candidate for hyperunification of the existing elementary forces.

© The Author(s) 2024

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