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

TL;DR

This paper explores how $SL(2N,C)$ gauge theories, constrained appropriately, can unify gravity with other fundamental forces, leading to an effective $SL(2,C) imes SU(N)$ symmetry and implications for grand unification and composite models.

Contribution

It introduces a covariant constraint in $SL(2N,C)$ theories that unifies gravity and gauge interactions, and applies this framework to composite models, identifying $SL(16,C)$ as a candidate for hyperunification.

Findings

Effective $SL(2,C) imes SU(N)$ symmetry emerges after removing redundant gauge components.

Many $SU(N)$ GUTs are irrelevant for standard spin 1/2 particles.

Among preon models, $SU(8)_L imes SU(8)_R$ satisfies anomaly matching, supporting a hyperunified $SL(16,C)$ symmetry.

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 $SL(2,C)\times SU(N)$ 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 $SU(N)_{L}\times SU(N)_{R}$ chiral symmetries of preons and their composites only the $SU(8)_{L}\times SU(8)_{R}$ meets the anomaly matching condition ensuring masslessness of these composites at large distances. This, in turn, identifies $SL(16,C)$ with the effective $SL(2,C)\times SU(8)$ symmetry, accommodating all three families of composite quarks and leptons, as the most likely candidate for hyperunification of the existing elementary forces.