- Superconformal algebra
In
theoretical physics , the superconformal algebra is agraded Lie algebra orsuperalgebra that combines theconformal algebra andsupersymmetry . It generates the superconformal group in some cases (In two Euclidean dimensions, theLie superalgebra doesn't generate anyLie supergroup .).In two dimensions, the superconformal algebra is infinite-dimensional. In higher dimensions, there is a finite number of known examples of superconformal algebras.
Superconformal algebra in 3+1D
According to [Citation
last = West
first = Peter C.
author-link =
title = "Introduction to rigid supersymmetric theories"
year = 1997
url = http://arxiv.org/abs/hep-th/9805055] [Citation
last = Gates
first = S. J.
author-link =Sylvester Gates
last2 = Grisaru
first2 = Marcus T.
author2-link =Marcus Grisaru
last3 = Rocek
first3 = M.
last4 = Siegel
first4 = W.
title = Superspace, or one thousand and one lessons in supersymmetry
journal = Front. Phys.
volume = 58
year = 1983
pages = 1-548
url = http://arxiv.org/abs/hep-th/0108200] ,the superconformal algebra in 3+1D is given by the bosonic generators , , , , the U(1)R-symmetry and the SU(N) R-symmetry and the fermionic generators , , and . denote spacetime indices, left-handed Weyl spinor indices and right-handed Weyl spinor indices, and the internal R-symmetry indices.The Lie superbrackets are given by:::::::::This is the bosonic conformal algebra. Here, η is the
Minkowski metric .::The bosonic conformal generators do not carry any R-charges.
::::
::::But the fermionic generators do.
::::::
Tells us how the fermionic generators transform under bosonic conformal transformations.
::::::
Superconformal algebra in 2D
See
super Virasoro algebra . There are two possible algebras; a Neveu-Schwarz algebra and a Ramond algebra.References
See also
*
conformal symmetry
*SUSY algebra
*Super Virasoro algebra
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