Coset space construction for the conformal group. I. Unbroken phase

TL;DR

This paper develops a coset space construction method for conformal theories, revealing how symmetries constrain Lagrangian forms and highlighting the role of Nambu-Goldstone fields for special conformal transformations.

Contribution

It introduces a new coset space approach for conformal invariance that clarifies the role of Nambu-Goldstone fields and symmetry constraints in conformal field theories.

Findings

Reproduces known conformal invariance consequences

Identifies fixed dependence of Nambu-Goldstone fields on coordinates

Derives constraints ensuring discrete symmetries in Lagrangians

Abstract

The technique for constructing conformally invariant theories within the coset space construction is developed. It reproduces all consequences of the conformal invariance and Lagrangians of widely-known conformal field theories. The method of induced representations, which plays the key role in the construction, allows to reveal a special role of the "Nambu-Goldstone fields" for special conformal transformations. Namely, their dependence on the coordinates turns out to be fixed by the symmetries. This results in the appearance of the constraints on possible forms of Lagrangians, which ensure that discrete symmetries are indeed symmetries of the theory.