Discrete gauge symmetries from (closed string) tachyon condensation

TL;DR

This paper demonstrates how discrete gauge symmetries in string theory can be embedded into continuous symmetries through supercritical extensions and tachyon condensation, revealing new insights into symmetry breaking and topological defects.

Contribution

It introduces a method to embed discrete symmetries into continuous ones in string theory using supercritical extensions and tachyon condensation, with explicit constructions and quantitative analysis.

Findings

Discrete symmetries embedded into continuous ones via supercritical strings.

Tachyon condensation breaks continuous symmetries, leaving discrete subgroups.

Charged topological defects realized as closed string tachyon solitons.

Abstract

The study of discrete gauge symmetries in field theory and string theory is often carried out by embedding them into continuous symmetries. Many symmetries however do not seem to admit such embedding, for instance discrete isometries given by large diffeomorphisms in compactifications. We show that in the context of string theory even those symmetries can be embedded into continuous ones. This requires extending the system to a supercritical string theory configuration with extra dimensions, on which the continuous symmetry acts. The extra dimensions are subsequently removed by closed string tachyon condensation, which breaks the continuous symmetry but preserves a discrete subgroup. The construction is explicit and the tachyon condensation can even be followed quantitatively for lightlike tachyon profiles. The embedding of discrete into continuous symmetries allows a realization of charged topological defects as closed string tachyon solitons, in tantalizing reminiscence of the construction of D-branes as open tachyon solitons.