K3 en route From Geometry to Conformal Field Theory
Abstract
To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their classification in low dimensions. I furthermore discuss CFT constructions for the simplest known examples that are based in Calabi-Yau geometry, namely for the toroidal superconformal field theories and their Z2-orbifolds. En route from geometry to CFT, I offer a discussion of K3 surfaces as the simplest class of Calabi-Yau manifolds where non-linear sigma model constructions bear mysteries to the very day. The elliptic genus in CFT and in geometry is recalled as an instructional piece of evidence in favor of a deep connection between geometry and conformal field theory.
Keywords
Cite
@article{arxiv.1503.08426,
title = {K3 en route From Geometry to Conformal Field Theory},
author = {Katrin Wendland},
journal= {arXiv preprint arXiv:1503.08426},
year = {2020}
}
Comments
39 pages, no figures; lecture notes for the author's contribution to the 2013 Summer School "Geometric, Algebraic and Topological Methods for Quantum Field Theory" in Villa de Leyva, Colombia