nLab superparticle

Idea

The superparticle is a sigma-model quantum field theory analogous to the ordinary relativistic particle but where either the worldline or the target space are taken to be supermanifolds. Described by supersymmetric quantum mechanics.

Definitions

One way to define what this means classically is to give an action functional on spaces of maps from the worldline into super target space. One such is the

• Green-Schwarz action functional.

The quantization of this action functional to a 1-dimensional worldvolume QFT is still largely an open problem.

An axiomatic description of the worldvolume QFT of the superparticle can be given in terms of FQFT as a representation of a category of super-cobordisms. One such approach is described at

• (1,1)-dimensional Euclidean field theories and K-theory.

The algebraic data encoded by such a representation is essentially that of a

• spectral triple.

See there for more details.

Related concepts

• super p-brane

• kappa-symmetry

• sigma model, brane

  • particle, spinning particle, fermion, superparticle

  • string

  • membrane

• string theory FQA – Does string theory predict supersymmetry?

References

Analysis in classical field theory in terms of supergeometry is in

• Daniel Freed, lecture 4 of Classical field theory and Supersymmetry, IAS/Park City Mathematics Series Volume 11 (2001) (pdf)

The pure spinor superparticle:

• Nathan Berkovits, Eduardo Casali, Max Guillen, Lionel Mason, Notes on the $D=11$ pure spinor superparticle (arXiv:1905.03737)

In a super-background field:

• Yu.A. Markov, M.A. Markova, A.I. Bondarenko, N.Yu. Markov, Superparticle in an external chiral matter superfield &lbrackhttps://arxiv.org/abs/2209.11565]