nLab superstring

Idea

The superstring 2-dimensional sigma-model is the analog of the string $\sigma$-model but with local worldsheet supersymmetry.

This is the higher dimensional analog of how the superparticle is related to the ordinary relativistic particle.

There are several different incarnations of the superstring.

• the spinning string or NSR string has in fact local worldsheet supersymmetry

  depending on how the GSO projection is chosen, this yields the type II superstring or type I superstring or type 0 superstring;

• the Green-Schwarz superstring instead has manifest target space supersymmetry.

• a mixture between the two has been proposed: the Berkovits superstring .

manifest supersymmetry for brane sigma-models:

manifest worldvolume supersymmetry	manifest target+worldvolume supersymmetry	manifest target space supersymmetry
NSR action functional	superembedding approach	Green-Schwarz action functional

graphics grabbed from FSS19c

Related concepts

• sigma-model, supersymmetric sigma-model, brane

  • relativistic particle, spinning particle, superparticle

  • string, spinning string,

  • superstring

    • super Riemann surface

    • Goddard-Thorn no-ghost theorem

    • 2d SCFT

      • 2-spectral triple, Dirac-Ramond operator

      • Gepner model, flop transition

    • type II superstring, type I superstring, heterotic superstring

    • superstring in 3d

    • Freed-Witten anomaly cancellation

    • string theory FAQ – Does string theory predict supersymmetry?

  • membrane

• string theory, supersymmetry

• string scattering amplitude

• 2d supergravity

manifest supersymmetry for brane sigma-models:

manifest worldvolume supersymmetry	manifest target+worldvolume supersymmetry	manifest target space supersymmetry
NSR action functional	superembedding approach	Green-Schwarz action functional

graphics grabbed from FSS19c

References

General

The relationship between the NRS spinning string and the Green-Schwarz superstring sigma-models is discussed in

• Rafael I. Nepomechie, Nonabelian bosonization, triality, and superstring theory Physics Letters B Volume 178, Issues 2-3, 2 October 1986, Pages 207-210

• I. Bars, D. Nemschansky and S. Yankielowicz, SLACPub- 3758.

This involves the relation between the octonion algebra and spinors in 2+8 dimensions (see also division algebra and supersymmetry):

• H. Tachibana, K. Imeda, Octonions, superstrings and ten-dimensional spinors , Il nuovo cimento, Vol 104 B N.1

• Yuhma Asano: Quantisation of type IIB superstring theory and the matrix model [arXiv:2408.04000]

Superspace and superembedding formalism

Discussion of the superstring equations of motion in superspace is due to

• Igor Bandos, Dmitrij Sorokin, Dmitrij Volkov, On the generalized action principle for superstrings and supermembranes, Phys. Lett. B352:269-275, 1995 (arXiv:hep-th/9502141)

and discussion via the superembedding formalism

• Igor Bandos, Paolo Pasti, Dmitri Sorokin, Mario Tonin, Dmitry Volkov, Chapter 4 of Superstrings and supermembranes in the doubly supersymmetric geometrical approach, Nucl. Phys. B446:79-118, 1995 (arXiv:hep-th/9501113)

Discussion of the superstring Green-Schwarz sigma-model in the broader context of The brane bouquet:

• C. Chrysso‌malakos, José de Azcárraga, José M. Izquierdo, C. Pérez Bueno, The geometry of branes and extended superspaces, Nucl. Phys. B 567 (2000) 293-330 [arXiv:hep-th/9904137, doi:10.1016/S0550-3213(99)00512-X]

• Domenico Fiorenza, Hisham Sati, Urs Schreiber, Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields, International Journal of Geometric Methods in Modern Physics, Volume 12, Issue 02 (2015) 1550018 (arXiv:1308.5264)