Conformal transformations of the S-matrix; $\beta$-function identifies change of spacetime

TL;DR

This paper derives conformal transformations of the S-matrix in massless phi^4 theory, revealing a hidden symmetry linked to a new spacetime structure characterized by a non-trivial conformal metric, identified through the beta function.

Contribution

It introduces a novel interpretation of anomalous conformal transformations as a symmetry involving a local coupling and a new spacetime geometry, connected via the beta function.

Findings

Conformal transformations of the S-matrix are explicitly derived.

Anomalous transformations can be recast as a symmetry with a local coupling.

A new spacetime with a non-trivial conformal metric is identified through the beta function.

Abstract

First conformal transformations of the $S$-matrix are derived in massless $\phi^4$-theory. Then it is shown that the anomalous transformations can be rewritten as a symmetry once one has introduced a local coupling and interprets the charge of the symmetry accordingly. By introducing a suitable effective coupling on which the $S$-matrix depends one is able to identify via the $\beta$-function an underlying new spacetime with non-trivial conformal (flat) metric.