# Coset space construction and inverse Higgs phenomenon for the conformal group

## TL;DR

This paper demonstrates how conformally invariant theories can be constructed using coset space methods, clarifies the role of Nambu-Goldstone fields, and questions the traditional use of inverse Higgs constraints in this context.

## Contribution

It introduces a coset space construction for conformal theories, clarifies the role of Nambu-Goldstone fields, and challenges the standard application of inverse Higgs constraints.

## Key findings

- Conformally invariant theories can be systematically constructed via coset space methods.
- Nambu-Goldstone fields for special conformal transformations ensure symmetry consistency.
- The use of inverse Higgs constraints in spontaneously broken conformal symmetry is questioned.

## Abstract

It is shown that conformally invariant theories can be obtained within the framework of the coset space construction. The corresponding technique is applicable for the construction of representations of the unbroken conformal group, as well as of a spontaneously broken one. A special role of the "Nambu-Goldstone fields" for special conformal transformations is clarified - they ensure self-consistency of a theory by guaranteeing that discrete symmetries are indeed symmetries of the theory. A generalization of the developed construction to a special class of symmetry groups with a non-linear realization of its discrete elements is given. Based on these results, the usage of the inverse Higgs constraints for the conformal group undergoing spontaneous symmetry breaking is questioned.