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Supersymmetry algebras in 1 + 1 dimensions

A two dimensional Minkowski space, i.e. a flat space with one time and one spacial dimension, has a two-dimensional Poincaré group IO(1,1) as its symmetry group. [1]

Central charge

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators.

Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.

Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

Lie algebra extension

In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension is an enlargement of a given Lie algebra by another Lie algebra.

Lie superalgebra

In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading.

Lorentz transformation

In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

Spacetime symmetries

Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry.

Super-Poincaré algebra

In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions.

Supercharge

In theoretical physics, a supercharge is a generator of supersymmetry transformations.

Supersymmetry

In particle physics, supersymmetry (SUSY) is a theory that proposes a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.

Supersymmetry algebra

In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions.

References

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