Conformal Smectics and their Many Metrics

TL;DR

This paper reveals that smectic liquid crystal configurations possess an infinite-dimensional conformal symmetry and establishes a connection with null hypersurfaces in symmetric spacetimes, enabling symmetry restoration through conformal factors.

Contribution

It introduces a novel conformal symmetry framework for smectics and links their structures to null hypersurfaces in maximally-symmetric spacetimes, expanding understanding of their geometric properties.

Findings

Equally-spaced smectics have an infinite-dimensional conformal symmetry.

A natural map exists between smectics and null hypersurfaces in symmetric spacetimes.

Appropriate conformal factors can restore symmetries of focal structures.

Abstract

We establish that equally-spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally-symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates.