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978-3-8439-2357-6, Reihe Physik

Maike Tormählen
Yang-Mills Solutions on Manifolds with G-Structure

143 Seiten, Dissertation Universität Hannover (2015), Hardcover, B5

Zusammenfassung / Abstract

This thesis addresses the construction of non-BPS Yang-Mills solutions and instantons on cones and cylinders over compact G-structure manifolds. These spaces play a key role in heterotic string compactifications, and many explicitly known examples are quotients of Lie groups. Explicit instanton solutions can serve as building blocks for heterotic supergravity solutions.

After the introduction of technical basics, in particular the geometry of coset spaces and G-structure manifolds, Yang-Mills theory as well as connections in tangent and principal bundles, the thesis turns to the construction of instanton solutions on cones over general coset spaces and over explicit examples. Solutions from earlier works are reproduced, and we find that the cone over the SU(3)-structure manifold SU(3)/(U(1)×U(1)) may potentially admit new instanton solutions.

In the next step, the Yang-Mills equation is written out with a special ansatz for the gauge connection, and explicit solutions on the cone over a general coset space are presented. We finally turn to cylinders over Sasakian manifolds, which allow for the construction of numerical and analytic Yang-Mills solutions as well as dyons and sphalerons.