superalgebra and (synthetic ) supergeometry
Super-conformal field theory in dimension , 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).
See at supersymmetry – Classification – Superconformal algebra – In dimension 2.
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
Lance Dixon, Paul Ginsparg, and Jeffrey Harvey, Superconformal field theory (pdf)
Yasuyuki Kawahigashi, Superconformal Field Theory
and Operator Algebras_ (pdf)
A hint for a relation to tmf, vaguely in line with the lift of the Witten genus to the string orientation of tmf:
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
Jürg Fröhlich, Krzysztof Gawędzki, Conformal Field Theory and Geometry of Strings, extended lecture notes for lecture given at the Mathematical Quantum Theory Conference, Vancouver, Canada, August 4-8 (arXiv:hep-th/9310187)
Yan Soibelman, Collapsing CFTs, spaces with non-negative Ricci curvature and nc-geometry , in Hisham Sati, Urs Schreiber (eds.), Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics, AMS (2001)
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.