Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model

TL;DR

This paper develops a gauge theory of gravity based on four one-dimensional unitary symmetries, unifying gravity with the Standard Model framework and addressing renormalizability and quantum corrections.

Contribution

It introduces a novel gauge theory of gravity using compact symmetries, aligning gravitational interaction with Standard Model gauge theories and exploring its quantum properties.

Findings

Unified gravity derived from four U(1) symmetries

Equivalent of general relativity obtained in Weitzenb"ock gauge

Infinities in quantum corrections can be renormalized

Abstract

The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has been challenging due to incompatibilities of the underlying theories - general relativity and quantum field theory. While quantum field theory utilizes compact, finite-dimensional symmetries associated with the internal degrees of freedom of quantum fields, general relativity is based on noncompact, infinite-dimensional external space-time symmetries. The present work derives the gauge theory of gravity using compact, finite-dimensional symmetries in a way that resembles the formulation of the fundamental interactions of the Standard Model. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field. Four U(1) symmetries of the space-time dimension field are used to derive a gauge theory, called unified gravity. The teleparallel equivalent of general relativity in the Weitzenb\"ock gauge is obtained from unified gravity by a gravity-gauge-field-dependent geometric condition. Unified gravity also enables a gravity-gauge-field-independent geometric condition that preserves the Minkowski metric. This differs from the use of metric in general relativity, where the metric depends on the gravitational field by definition. We study the renormalizability and radiative corrections of the theory at 1-loop order. The equivalence principle is formulated by requiring that the renormalized values of the inertial and gravitational masses are equal. In contrast to previous theories of gravity, all infinities that are encountered in the calculations of loop diagrams can be absorbed by the redefinition of the small number of parameters of the theory in the same way as in the gauge theories of the Standard Model.