Quantum order from string-net condensations and origin of light and massless fermions

TL;DR

This paper explains how quantum orders and string-net condensation in local bosonic models give rise to massless gauge bosons and fermions, providing a unified framework for understanding light and massless particles.

Contribution

It demonstrates that quantum orders can be viewed as string-net condensed states, linking gauge bosons and fermions to string-net fluctuations and ends.

Findings

Gauge bosons are fluctuations of condensed closed strings.

Ends of open strings act as charged particles, including fermions.

Emergence of chiral symmetry from quantum order's projective symmetry.

Abstract

Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this paper, we demonstrate that a state with such kind of quantum orders can be viewed as a string-net condensed state. The emerging gauge bosons and fermions in local bosonic models can be regarded as a direct consequence of string-net condensation. The gauge bosons are fluctuations of nets of large closed strings which are condensed in the ground state. The ends of condensed open strings are the charged particles of the corresponding gauge field. For certain types of strings, the ends of strings can even be fermions. According to the string-net picture, fermions always carry gauge charges. This suggests the existence of a new discrete gauge field that couples to neutrinos and neutrons. We also discuss how chiral symmetry that protects massless Dirac fermions can emerge from the projective symmetry of quantum order.