M-Theory on Spin(7) Manifolds

TL;DR

We study M-theory on Spin$(7)$ manifolds with isolated conical singularities, constructing a new non-compact Spin$(7)$ family on the universal quotient bundle ${\mathcal Q}$ over ${\bf \mathbb{C}P}^2$ and detailing their topology via Aloff-Wallach level surfaces. A central result is the appearance of half-integer $G$-flux quantisation, arising from global anomalies and K-theory, and its direct link to induced Chern-Simons terms in the three-dimensional ${\cal N}=1$ effective theory, realized through D6-branes wrapped on coassociative cycles and Spin$^c$ structures. The work establishes precise correspondences between M-theory charges and Type IIA D-brane configurations, including isomorphisms $H^2(L)\cong H^4(X)$ and $H^3(L)\cong H^5(X)$, and shows how Spin$(7)$ geometry and flux data are controlled by Aloff-Wallach spaces. The explicit analyses of the ${\mathbb B}_8$ and ${\mathcal Q}$ models reveal parity-violating CS terms, mass gaps, and potential AdS$_4$ connections, highlighting the physical significance of Spin$(7)$ holonomy in three-dimensional gauge dynamics and holography.

Abstract

We study M-theory on two classes of manifolds of Spin(7) holonomy that are developing an isolated conical singularity. We construct explicitly a new class of Spin(7) manifolds and analyse in detail the topology of the corresponding classical spacetimes. We discover also an intricate interplay between various anomalies in M-theory, string theory, and gauge theory within these models, and in particular find a connection between half-integral G-fluxes in M-theory and Chern-Simons terms of the N=1, D=3 effective theory.