Effective Field Theories for Local Models in F-Theory and M-Theory

TL;DR

The paper investigates a strict locality hypothesis for visible-sector phenomenology in F-theory and M-theory, arguing that in the $M_{Pl}\to\infty$ limit bulk gravity decouples and local geometry fully determines the EFT. It recasts high-scale physics in purely group-theoretic terms, identifying $G$-adjoint branching into $H\times U_1^1\times\cdots\times U_1^k$ (often starting from $E_8$) as the core organizing principle, and provides concrete rules for constructing locally engineerable models. It contrasts the flexible flux-based chirality in F-theory with the more constrained M-theory spectrum, and discusses implications for Yukawas, superpotential sparsity, and anomaly cancellation via Green-Schwarz axions. The work highlights natural hierarchies and a network of extra $U(1)$-descended symmetries that can suppress unwanted operators, including a PQ-like axion, offering concrete, testable structure to low-energy phenomenology. Overall, locality sharply restricts the high-energy landscape and yields actionable predictions for the SM’s embedding in string theory.

Abstract

Requiring a strictly local origin of visible sector phenomenology is perhaps the strongest, most falsifiable condition that one can impose on string theory at the high scale: it at once excludes a vast majority of the string landscape, and yet leads naturally to constructions that can be surprisingly realistic (and familiar). Yet only for local models can gravity be made parametrically weak while keeping the strength of gauge- and Yukawa-couplings fixed--a limit which is well-motivated by low-energy experiments. Conveniently, the entire class of high-scale effective field theories that can arise from such local models in F-theory and M-theory can be classified according to simple, purely group-theoretic rules. In this note, we describe these rules from the viewpoint of an effective field theorist with little interest in the underlying geometry or high-scale physics, and we discuss the general predictions these models have for low-energy phenomenology.