nLab fundamental M2-brane sigma-model -- references

Super-membrane/M2-brane as a sigma model

The Green-Schwarz sigma-model-type formulation of the super-membrane in 11d (as in the brane scan and in contrast to the black brane-solutions of 11d supergravity) first appears in:

• Eric Bergshoeff, Ergin Sezgin, and Paul Townsend, Supermembranes and eleven-dimensional supergravity, Phys. Lett. B 189 (1987) 75-78 [doi:10.1016/0370-2693(87)91272-X, spire:248230]

Via the superembedding approach the equations of motion were obtained in

• Igor Bandos, Paolo Pasti, Dmitri Sorokin, Mario Tonin, Dmitry Volkov, Chapter 3 of Superstrings and supermembranes in the doubly supersymmetric geometrical approach, Nucl. Phys. B446:79-118, 1995 (arXiv:hep-th/9501113)

and the Lagrangian density in:

• Paul Howe, Ergin Sezgin, The supermembrane revisited, Class. Quant. Grav. 22 (2005) 2167-2200 [arXiv:hep-th/0412245, doi:10.1088/0264-9381/22/11/017]

The double dimensional reduction of the M2-brane to the Green-Schwarz superstring was observed in

• Michael Duff, Paul Howe, T. Inami, Kellogg Stelle, Superstrings in $D=10$ from Supermembranes in $D=11$, Phys. Lett. B 191 (1987) 70 [doi:10.1016/0370-2693(87)91323-2]

  also in: Michael Duff (ed.): The World in Eleven Dimensions 205-206 (1987) [spire:245249]

• Paul Townsend, The eleven-dimensional supermembrane revisited, Phys. Lett. B 350 (1995) 184-187 [arXiv:hep-th/9501068, doi:10.1016/0370-2693(95)00397-4]

around the time when M-theory became accepted due to

• Edward Witten, String Theory Dynamics In Various Dimensions (arXiv:hep-th/9503124)

See also

• Igor Bandos, Paul Townsend, SDiff Gauge Theory and the M2 Condensate (arXiv:0808.1583)

• Maria P. Garcia del Moral, C. Las Heras, P. Leon, J. M. Pena, Alvaro Restuccia, Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes, J. High Energ. Phys. 2020 97 (2020) [arXiv:2005.06397, doi:10.1007/JHEP09(2020)097]

Discussion from the point of view of Green-Schwarz action functional-∞-Wess-Zumino-Witten theory:

• Domenico Fiorenza, Hisham Sati, Urs Schreiber, Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields (2013)

On possible structures in M2-brane dynamics and M2-M5-brane bound states which could be M-theory-lifts of the familiar integrability of the Green-Schwarz superstring on $AdS_5$ $\times$ $S^5$:

• Kirill Gubarev, Edvard Musaev, Integrability structures in string theory [arXiv:2301.06486]