Pattern quarks and leptons

Abstract

Disclinations, concave and convex, are the canonical point defects of two-dimensional planar patterns in systems with translational and rotational symmetries. From these, all other point defects (vortices, dislocations, targets, saddles and handles) can be built. Moreover, handles, coupled concave–convex disclination pairs arise as instabilities, symmetry breaking events. The purpose of this article is to show that embedded in three or more dimensions, concave and convex disclination strings, two-dimensional disclinations with loop backbones, have interesting and suggestive invariant indices which are integer multiples of and .

Keywords:

• disclinations
• quarks
• leptons

AMS Subject Classifications::

• 35B36

Acknowledgements

This work was supported by NSF grant DMS 0906024 in the proposal for which the notion of pattern quarks and leptons was first suggested.