In theoretical physics
, the superconformal algebra is a graded Lie algebra
that combines the conformal algebra
. It generates the superconformal group
in some cases (In two Euclidean dimensions, the Lie superalgebra
doesn't generate any Lie 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 ,
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
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.