A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory

TL;DR

This paper introduces a superconnection framework based on the supergroup 2(P)(4,R) that spontaneously breaks to 2(SO)(1,3), deriving Einstein's gravity as an effective low-energy theory with promising renormalizability and unitarity.

Contribution

It proposes a novel superconnection approach using 2(P)(4,R) to unify Riemannian and post-Riemannian gravity, leading to Einstein's theory as a low-energy limit.

Findings

Superconnection formalism unifies gauge and Higgs fields in gravity.

Spontaneous symmetry breaking yields Einstein gravity as an effective theory.

The resulting theory is potentially renormalizable and unitary.

Abstract

A superconnection is a supermatrix whose even part contains the gauge-potential one-forms of a local gauge group, while the odd parts contain the (0-form) Higgs fields; the combined grading is thus odd everywhere. We demonstrate that the simple supergroup ${\bar P}(4,R)$ (rank=3) in Kac' classification (even subgroup $\bar {SL}(4,R)$) prverline {SL}(4,R)$) provides for the most economical spontaneous breaking of $\bar{SL}(4,R)$ as gauge group, leaving just local $\bar{SO}(1,3)$ unbroken. As a result, post-Riemannian SKY gravity yields Einstein's theory as a low-energy (longer range) effective theory. The theory is renormalizable and may be unitary.