On the Quantum Moduli Space of M Theory Compactifications

TL;DR

The paper addresses the quantum moduli space of M-theory on G_2 manifolds asymptotic to cones over quotients of ${\bf S}^3 \times {\bf S}^3$, showing the space splits into branches labeled by the number of massless ${U(1)}$ factors and connects semiclassical points with different gauge groups. It develops a unified framework using holomorphic observables ${\eta}_j$ built from $f_j$ and $C$-field periods, and derives a quantum curve governed by membrane instantons that links classical geometry to quantum physics. By analyzing quotients $Y_\Gamma$ with ADE groups, it reveals how low-energy gauge theories arise on different loci and how their phases connect across the moduli space, including extra semiclassical points for the $D$ and $E$ series. The work generalizes prior results to a broad class of quotients and provides a detailed map between geometry of the seven-manifold, C-field data, and the resulting 4d supersymmetric gauge theories. This deepens our understanding of nonperturbative M-theory dynamics and the landscape of consistent 4d theories emerging from G_2 compactifications.

Abstract

We study the moduli space of M-theories compactified on G_2 manifolds which are asymptotic to a cone over quotients of S^3 x S^3. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U(1) factors. Each component smoothly interpolates among supersymmetric gauge theories with different gauge groups.