Abstract
Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by non-commuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure "hidden" in T-branes.
Highlights
Manifolds of special holonomy are of great importance in connecting the higher-dimensional spacetime predicted by string theory to lower-dimensional physical phenomena
Compactifications of string/M-F-theory on manifolds of special holonomy produce a wide variety of novel physical systems
In this paper we have used methods from threeand two-dimensional gauge theory to study a broad class of examples in which some important features of the background are captured by non-Abelian data, namely T-brane configurations
Summary
Manifolds of special holonomy are of great importance in connecting the higher-dimensional spacetime predicted by string theory to lower-dimensional physical phenomena. Reasonable to expect that degenerations in the CalabiYau building blocks will provide a way to generate the long sought for codimension six and seven singularities in compact models From this perspective, one might ask whether this is the most general starting point one can entertain for realizing localized matter in G2 compactifications. This points the way to a method for constructing G2 backgrounds using more general holomorphic building blocks than those appearing in the classical TCS construction Another feature we study in great detail is the resulting localized matter obtained from such T-brane configurations.
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