Continuous Global Symmetries and Hyperweak Interactions in String Compactifications

TL;DR

The paper analyzes why exact continuous global symmetries are absent in string compactifications and extends the Banks–Dixon argument to include D-brane (open-string) sectors. It shows closed strings gauge exact global symmetries, while open strings can host approximate global symmetries when gravity decouples, identifying two robust mechanisms in LARGE volume models: approximate non-Abelian flavour symmetries from local Calabi–Yau isometries, and hyperweak gauge interactions from bulk branes. The authors show that approximate flavour symmetries can arise with a breaking parameter $R_s/R_b\sim 0.01$, potentially linking fermion mass hierarchies to the large-volume geometry, while hyperweak gauge groups yield ultra-weak couplings that could mix with the SM. These insights have implications for low-energy phenomenology and guide experimental searches for new, feebly interacting sectors.

Abstract

We revisit general arguments for the absence of exact continuous global symmetries in string compactifications and extend them to D-brane models. We elucidate the various ways approximate continuous global symmetries arise in the 4-dimensional effective action. In addition to two familiar methods - axionic Peccei-Quinn symmetries and remnant global abelian symmetries from Green-Schwarz gauge symmetry breaking - we identify new ways to generate approximate continuous global symmetries. Two methods stand out, both of which occur for local brane constructions within the LARGE volume scenario of moduli stabilisation. The first is the generic existence of continuous non-abelian global symmetries associated with local Calabi-Yau isometries. These symmetries are exact in the non-compact limit and are spontaneously broken by the LARGE volume, with breaking effects having phenomenologically interesting sizes \sim 0.01 for plausible choices for underlying parameters. Such approximate flavour symmetries are phenomenologically attractive and may allow the fermion mass hierarchies to be connected to the electroweak hierarchy via the large volume. The second is the possible existence of new hyper-weak gauge interactions under which Standard Model matter is charged, with α_{HW} \sim 10^{-9}. Such groups arise from branes wrapping bulk cycles and intersecting the local (resolved) singularity on which the Standard Model is supported. We discuss experimental bounds for these new gauge bosons and their interactions with the Standard Model particles.