[Paper Review] General Structure of Conformal Anomaly and 4 Dimensional Photon-Dilaton Gravity

Shoichi Ichinose|ArXiv.org|Jan 10, 1998

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper provides a rigorous proof that the conformal anomaly remains conformally invariant in classically conformal field theories using heat-kernel regularization and Fujikawa's method. It derives a new explicit expression for the conformal anomaly in 4D photon-dilaton gravity, analyzing the dilaton's role in the anomaly's general structure, offering a deeper understanding of quantum corrections in conformal gravity models.

ABSTRACT

The general structure of the conformal anomaly and the dilaton's effect to it are analysed. First we give a new formal proof of the statement that the conformal anomaly, in the theory which is conformal invariant at the classical level, is conformal invariant. The heat-kernel regularization and Fujikawa's method are taken for the analysis. We present a new explicit result of the conformal anomaly in 4 dimensional photon-dilaton gravity. This result is examined from the point of the general structure.

Motivation & Objective

• To rigorously establish the conformal invariance of the conformal anomaly in quantum field theories that are classically conformal.
• To analyze the role of the dilaton field in modifying or preserving the structure of the conformal anomaly.
• To derive an explicit, closed-form expression for the conformal anomaly in four-dimensional photon-dilaton gravity.
• To examine the general structure of the anomaly in the context of effective field theory and quantum gravity.

Proposed method

• Employing heat-kernel regularization to systematically compute quantum corrections in the presence of gauge and gravitational fields.
• Applying Fujikawa's method to trace the anomaly to the Jacobian of the path integral measure under conformal transformations.
• Constructing a 4D effective action for photon-dilaton gravity coupled to matter fields, preserving classical conformal symmetry.
• Using covariant techniques to ensure gauge and diffeomorphism invariance in the regularization procedure.
• Deriving the anomaly tensor from the trace anomaly via the Weyl anomaly equation.
• Analyzing the dilaton coupling to the curvature and gauge fields to determine its impact on the anomaly structure.

Experimental results

Research questions

• RQ1 Does the conformal anomaly remain invariant under conformal transformations in a theory that is classically conformal?
• RQ2 How does the dilaton field modify the structure of the conformal anomaly in 4D gravity coupled to photons?
• RQ3 What is the explicit form of the conformal anomaly in 4D photon-dilaton gravity?
• RQ4 Can the general structure of the anomaly be consistently derived using heat-kernel and Fujikawa methods?
• RQ5 What are the implications of the dilaton's presence for the renormalization and quantum consistency of conformal gravity?

Key findings

• The conformal anomaly is proven to be conformally invariant in classically conformal field theories using both heat-kernel and Fujikawa methods.
• A new explicit expression for the conformal anomaly is derived in 4D photon-dilaton gravity, valid in the presence of background gauge and gravitational fields.
• The dilaton couples non-minimally to the curvature and gauge fields, modifying the anomaly structure in a way consistent with conformal symmetry.
• The anomaly tensor is shown to transform covariantly under Weyl rescalings, confirming its conformal invariance.
• The result is consistent with the general structure of the Weyl anomaly and provides a concrete realization in a specific 4D effective theory.
• The analysis confirms that the anomaly is independent of the regularization scheme as long as conformal invariance is preserved at the quantum level.