nLab superconformal geometry

Idea

The joint generalization of conformal geometry and supergeometry.

Classification

See at Supersymmetry – Classification of superconformal algebras

Related concepts

• supersymmetry

• superconformal super Lie group

• superconformal field theory

References

General

• Werner Nahm, Supersymmetries and their Representations, Nucl.Phys. B135 (1978) 149 (spire, pdf)

• Steven Shnider, The superconformal algebra in higher dimensions, Letters in Mathematical Physics November 1988, Volume 16, Issue 4, pp 377-383

• Andree Lischewski, Conformal superalgebras via tractor calculus, Class.Quant.Grav. 32 (2015) 015020 (spire, arXiv:1408.2238)

• Conformal and superconformal symmetries [pdf]

Generalization to local superconformal algebras:

• Fabian Hahner, Surya Raghavendran, Ingmar Saberi, Brian R. Williams: Local superconformal algebras [arXiv:2410.08176]

In dimension $6 = 5+1$

Discussion of the superconformal symmetry group, the orthosymplectic supergroup $OSp(8^\ast,2N)$, includes

• Sergio Ferrara, Emery Sokatchev, Representations of superconformal algebras in the $AdS_{7/4}/CFT_{6/3}$ correspondence, J.Math.Phys. 42 (2001) 3015-3026 (arXiv:hep-th/0010117)

• Murat Gunaydin, Seiji Takemae, Unitary Supermultiplets of $OSp(8^*|4)$ and the $AdS_7/CFT_6$ Duality, Nucl. Phys. B 578 (2000) 405–448, Erratum-ibid. B 697 (2004) 399–402 [arXiv:hep-th/9910110]