nLab
2d SCFT

Contents

Context

Quantum field theory

String theory

Super-Geometry

Contents

Idea

Super-conformal field theory in dimension d=2d = 2, locally given by a super vertex operator algebra.

For central charge 15 this is the worldsheet theory of the superstring.

May be regarded as a “2-spectral triple” (see there for more), the 2-dimensional generalization of spectral triples describing the quantum mechanics of spinning particles (super-particles).

Examples

Properties

Classification

See at supersymmetry – Classification – Superconformal algebra – In dimension 2.

References

General

A basic but detailed exposition focusing on the super-WZW model (and the perspective of 2-spectral triples) is in Fröhlich Gawedzki 93

Other accounts include

A hint for a relation to tmf, vaguely in line with the lift of the Witten genus to the string orientation of tmf:

Relation to 2-spectral triples

Discussion of 2d SCFTs as a higher analog of spectral triples (“2-spectral triples”, see there for more) is in terms of vertex operator algebras in

and in terms of conformal nets in

Last revised on November 5, 2018 at 03:48:19. See the history of this page for a list of all contributions to it.