nLab membrane




The next higher dimensional generalization of the concept of a relativistic particle and a relativistic string is called the relativistic membrane.

The concept of a bosonic membrane was considered already by Dirac 62 as a hypothetical model for the electron, then abandoned and eventually re-incarnated as the “super-membrane in 11d” due to Bergshoeff-Sezgin-Townsend 87 (whose “m” became the “M” in “M-theory”), namely the Green-Schwarz sigma-model for super p-branes corresponding to the brane scan-entry with p=2p=2, D=11D=11, now commonly known as the M2-brane.

In fact, according to the brane scan, a super 2-brane sigma model exists on superspacetimes of dimension 4, 5, 7, and 11:



Early speculations trying to unify the electron and the muon as two excitations of a single relativistic membrane:

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:

Via the superembedding approach the equations of motion were obtained in

and the Lagrangian density in:

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

around the time when M-theory became accepted due to

See also

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

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 AdS_5 ×\times S 5 S^5 :

Quantization of the M2-brane sigma-model to a matrix model

The Poisson bracket-formulation of the classical light-cone gauge Hamiltonian for the bosonic relativistic membrane and the corresponding matrix commutator regularization is due to:

Some exact solutions:

On the regularized light-cone gauge quantization of the Green-Schwarz sigma model for the M2-brane on (super) Minkowski spacetime, yielding the BFSS matrix model:

Original articles:

Observation that the spectrum is continuous:


The generalization to pp-wave spacetimes (leading to the BMN matrix model):

See also

A new kind of perturbation series for the quantized super-membrane:

Relation to the string dilaton under double dimensional reduction:

Last revised on June 16, 2023 at 11:32:37. See the history of this page for a list of all contributions to it.