Discrete gauge symmetries in D-brane models

TL;DR

The paper investigates how discrete gauge symmetries arise naturally in string-based brane constructions, arguing that Zn remnants of continuous U(1) factors with BF couplings are generic and robust against nonperturbative effects. It develops a precise BF-coupling framework to derive Zn survival conditions, analyzes instanton effects, and confirms anomaly cancellation for these discrete symmetries. Applying the framework to MSSM-like brane models and local SU(5) GUT/F-theory setups, the authors show R-parity, baryon triality, and related Zn symmetries emerge as anomaly-free remnants and can forbid dangerous B- and L-violating operators while preserving required Yukawas. They also connect these results to F-theory GUTs via spectral-cover fluxes and note K-theory Z2 constraints as a potential source of R-parity, outlining directions for extending the analysis to other setups and non-Abelian discrete symmetries.

Abstract

In particle physics model building discrete symmetries are often invoked to forbid unwanted or dangerous couplings. A classical example is the R-parity of the MSSM, which guarantees the absence of dimension four baryon- and lepton-number violating operators. Although phenomenologically useful, these discrete symmetries are, in the context of field theory, poorly motivated at a more fundamental level. Moreover, discrete {\em global} symmetries are expected to be violated in consistent couplings to quantum gravity, while their {\em gauged} versions are expected to actually exist. In this paper we study discrete gauge symmetries in brane models in string theory, and argue that they are fairly generic in this framework. In particular we study the appearance of discrete gauge symmetries in (MS)SM brane constructions in string theory, and show that a few discrete ${Z_N}$ gauge symmetries, including R-parity and {\it baryon triality}, appear naturally as remnants of continuous U(1) gauge symmetries with Stückelberg $N(B\wedge F)$ couplings. Interestingly, they correspond to the simplest anomaly-free discrete symmetries of the MSSM as classified in the early 90's. We provide a number of examples based on type IIA intersecting brane constructions with a (MS)SM spectrum. We also study the appearance of discrete generalizations of R-parity in unified SU(5) type IIA orientifolds and local F-theory SU(5) GUTs.