nLab
2d SCFT
Context
Quantum field theory
String theory
Ingredients
Critical string models
Extended objects
Topological strings
Backgrounds
Phenomenology
Super-Geometry
Contents
Idea
Super-conformal field theory in dimension $d = 2$ , 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 mechnanics of spinning particles (super-particles).

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

Table of branes appearing in supergravity /string theory (for classification see at brane scan ).

brane in supergravity charge d under gauge field has worldvolume theory black brane supergravity higher gauge field SCFT
D-brane type II RR-field super Yang-Mills theory
$(D = 2n)$ type IIA $\,$ $\,$
D0-brane $\,$ $\,$ BFSS matrix model
D2-brane $\,$ $\,$ $\,$
D4-brane $\,$ $\,$ D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane $\,$ $\,$ D=7 super Yang-Mills theory
D8-brane $\,$ $\,$
$(D = 2n+1)$ type IIB $\,$ $\,$
D(-1)-brane $\,$ $\,$ $\,$
D1-brane $\,$ $\,$ 2d CFT with BH entropy
D3-brane $\,$ $\,$ N=4 D=4 super Yang-Mills theory
D5-brane $\,$ $\,$ $\,$
D7-brane $\,$ $\,$ $\,$
D9-brane $\,$ $\,$ $\,$
(p,q)-string $\,$ $\,$ $\,$
(D25-brane ) (bosonic string theory )
NS-brane type I, II, heterotic circle n-connection $\,$
string $\,$ B2-field 2d SCFT
NS5-brane $\,$ B6-field little string theory
D-brane for topological string $\,$
A-brane $\,$
B-brane $\,$
M-brane 11D SuGra /M-theory circle n-connection $\,$
M2-brane $\,$ C3-field ABJM theory , BLG model
M5-brane $\,$ C6-field 6d (2,0)-superconformal QFT
M9-brane /O9-plane heterotic string theory
M-wave
topological M2-brane topological M-theory C3-field on G2-manifold
topological M5-brane $\,$ C6-field on G2-manifold
solitons on M5-brane 6d (2,0)-superconformal QFT
self-dual string self-dual B-field
3-brane in 6d

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

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

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

Revised on September 25, 2016 10:40:38
by

Urs Schreiber
(89.204.153.161)