Weyl gauge-vector and complex dilaton scalar for conformal symmetry and its breaking

TL;DR

This paper introduces a hybrid conformal gravity model using a complex dilaton and Weyl gauge-vector, addressing ghost issues and providing a mechanism for spontaneous symmetry breaking with potential cosmological implications.

Contribution

It proposes a novel hybrid conformal gravity framework combining a complex dilaton and Weyl gauge-vector, avoiding ghost problems and enabling spontaneous symmetry breaking.

Findings

Avoids ghost problem in dilaton kinetic term

Provides a mechanism for spontaneous conformal symmetry breaking

Suggests a mass scale for broken symmetry related to Planck mass

Abstract

Instead of the scalar "dilaton" field that is usually adopted to construct conformally invariant Lagrangians for gravitation, we here propose a hybrid construction, involving both a complex dilaton scalar and a Weyl gauge-vector, in accord with Weyl's original concept of a non-Riemannian conformal geometry with a transport law for length and time intervals, for which this gauge vector is required. Such a hybrid construction permits us to avoid the wrong sign of the dilaton kinetic term (the ghost problem) that afflicts the usual construction. The introduction of a Weyl gauge-vector and its interaction with the dilaton also has the collateral benefit of providing an explicit mechanism for spontaneous breaking of the conformal symmetry, whereby the dilaton and the Weyl gauge-vector acquire masses somewhat smaller than m/sub/P by the Coleman-Weinberg mechanism. Conformal symmetry breaking is assumed to precede inflation, which occurs later by a separate GUT or electroweak symmetry breaking, as in inflationary models based on the Higgs boson.