Snapshots of Conformal Field Theory

Abstract

In snapshots, this exposition introduces conformal field theory, with a focus on those perspectives that are relevant for interpreting superconformal field theory by Calabi-Yau geometry. It includes a detailed discussion of the elliptic genus as an invariant which certain superconformal field theories share with the Calabi-Yau manifolds. K3 theories are (re)viewed as prime examples of superconformal field theories where geometric interpretations are known. A final snapshot addresses the K3-related Mathieu Moonshine phenomena, where a lead role is predicted for the chiral de Rham complex.

43 pages; contribution to "Mathematical Aspects of Quantum Field Theories", Mathematical Physics Studies, Springer; v2: typos corrected, references added and updated

References in corpus (9)

• Notes on the K3 Surface and the Mathieu group M_24
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Note on Twisted Elliptic Genus of K3 Surface
• Chiral de Rham complex and the half-twisted sigma-model
• Mathieu Moonshine in the elliptic genus of K3
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Symmetry-surfing the moduli space of Kummer K3s
• A twist in the M24 moonshine story
• Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence

Cited by in corpus (6)

• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• A twist in the M24 moonshine story
• Hodge-elliptic genera and how they govern K3 theories
• SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs
• Not Doomed to Fail
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups