M theory and singularities of exceptional holonomy manifolds

By B. Acharya, Sergei Gukov. 2004

169 citations recorded by the source corpus.

M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c7a598b23c5b3d2430a4aff7c5b65afb38460f13

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In Applied Mathematics

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Fivebranes and 4-manifolds (2013, unknown): “[21] for a pedagogical review).”
The spinorial geometry of supersymmetric backgrounds (2004, background): “For example, one can define as M-theory G2 compactifications with fluxes as those on backgrounds that exhibit the Poincaré symmetry of four-dimensional Minkowski space, (compact internal space) and admit Killing spinors that have stability subgroup G2, see [40] for a review and [41] for the compacti”
G2-manifolds and associative submanifolds via semi-Fano 3-folds (2012, background): “To obtain realistic particle physics (ie non-abelian gauge groups and chiral fermions) from M-theory on G2-manifolds it appears necessary to consider singular G2-spaces with very particular kinds of singularity as explained in [1, 2, 7, 9].”
A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi–Hanson spaces (2017, background): “In particular, they are both Ricci-flat compact Riemannian manifolds, and they both admit parallel spinors, making them candidates for supersymmetric compactification spaces in physics [1].”