In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have N = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector.

There are two minimal extensions of the Virasoro algebra with N = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element C and generators L_m (for integer m) satisfying

${\displaystyle [L_{m},L_{n}]=(m-n)L_{m+n}+{\frac {c}{12}}m(m^{2}-1)\delta _{m+n,0}}$

where ${\displaystyle \delta _{i,j}}$ is the Kronecker delta.

The odd part of the algebra has basis ${\displaystyle G_{r}}$, where ${\displaystyle r}$ is either an integer (the Ramond case), or half an odd integer (the Neveu–Schwarz case). In both cases, ${\displaystyle c}$ is central in the superalgebra, and the additional graded brackets are given by

${\displaystyle [L_{m},G_{r}]=\left({\frac {m}{2}}-r\right)G_{m+r}}$

${\displaystyle \{G_{r},G_{s}\}=2L_{r+s}+{\frac {c}{3}}\left(r^{2}-{\frac {1}{4}}\right)\delta _{r+s,0}}$

Note that this last bracket is an anticommutator, not a commutator, because both generators are odd.