Discrete gauge symmetries from (closed string) tachyon condensation

TL;DR

This work shows that genuine discrete gauge symmetries in string theory can be realized as remnants of continuous symmetries by promoting the theory to supercritical dimensions and then removing them through closed-string tachyon condensation. The authors develop several mechanisms—via quenched rotations, quenched translations (mapping tori), and their dual descriptions—to embed discrete symmetries such as ${\mathbb Z}_n$ and non-abelian groups into continuous ones acting on extra dimensions, with the endpoint recovering the original critical theory and leaving a discrete subgroup. A central payoff is the realization of charged topological defects as closed-string tachyon solitons, drawing a parallel with D-branes as open-string tachyon solitons and suggesting KO-theory-like classifications for closed-string tachyons. The framework unifies diverse discrete symmetries (large isometries, orbifold quantum symmetries, T-duality twists, and antiholomorphic actions) and links them to a topologically controlled tachyon-condensation dynamics, offering new tools for analyzing discrete symmetries in string phenomenology and beyond.

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.