Toric Lego: A method for modular model building

TL;DR

The paper develops a modular, string-theoretic framework for embedding multiple interacting sectors—such as MSSM-like visible sectors, supersymmetry-breaking sectors, and dark matter sectors—into local Calabi–Yau geometries by joining branes at toric singularities via massive mediators. It provides a concrete algorithm (unresolving/joining) based on dimer models, zig-zag paths, and the fast inverse algorithm, with mediator masses tied to resolved-cycle sizes and tadpole constraints carefully addressed. A canonical three-sector toy model is constructed and analyzed, including a SUSY-breaking sector on $dP_1$, a trinified visible sector on $dP_0$, and a mirror dark sector, along with several modifications (flavor D7 branes, orientifolds) and a Type IIA mirror description via the amoeba/alga maps. The approach yields a calculable, flexible platform for exploring gauge mediation, interacting dark matter, and multi-sector phenomenology within a controlled local string-theory setting, with clear pathways to further realism and global embedding.

Abstract

Within the context of local type IIB models arising from branes at toric Calabi-Yau singularities, we present a systematic way of joining any number of desired sectors into a consistent theory. The different sectors interact via massive messengers with masses controlled by tunable parameters. We apply this method to a toy model of the minimal supersymmetric standard model (MSSM) interacting via gauge mediation with a metastable supersymmetry breaking sector and an interacting dark matter sector. We discuss how a mirror procedure can be applied in the type IIA case, allowing us to join certain intersecting brane configurations through massive mediators.