nLab quantization of M2-brane to matrix model -- references

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:

• Jens Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, MIT 1982 (dspace:1721.1/15717, pdf)

Some exact solutions:

• Jens Hoppe, Exact algebraic M(em)brane solutions $[$arXiv:2107.00569$]$

• Jens Hoppe, The fast non-commutative sharp drop $[$arXiv:2302.13146$]$

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:

• Bernard de Wit, Jens Hoppe, Hermann Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B 305 (1988) 545-581 [doi:10.1016/0550-3213(88)90116-2, spire:261702, pdf, pdf]

Observation that the spectrum is continuous:

• Bernard de Wit, W. Lüscher, Hermann Nicolai, The supermembrane is unstable, Nucl. Phys. B 320 (1989) 135 [doi:10.1016/0550-3213(89)90214-9, spire:266584]

Review:

• Hermann Nicolai, Robert C. Helling, Supermembranes and M(atrix) Theory, In: Trieste 1998, Nonperturbative aspects of strings, branes and supersymmetry (1998) 29-74 (arXiv:hep-th/9809103, spire:476366)

• Jens Hoppe, Membranes and Matrix Models [arXiv:hep-th/0206192]

• Arundhati Dasgupta, Hermann Nicolai, Jan Plefka, An Introduction to the Quantum Supermembrane, Grav. Cosmol. 8 1 (2002) and Rev. Mex. Fis. 49S1 (2003) 1-10 [arXiv:hep-th/0201182, spire:582067]

• Gijs van den Oord, On Matrix Regularisation of Supermembranes MSc thesis (2006) (pdf)

• Meer Ashwinkumar, Lennart Schmidt, Meng-Chwan Tan, Section 2 of: Matrix Regularization of Classical Nambu Brackets and Super $p$-Branes (arXiv:2103.06666)

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

• Keshav Dasgupta, Mohammad Sheikh-Jabbari, Mark Van Raamsdonk, Section 2 of: Matrix Perturbation Theory For M-theory On a PP-Wave, JHEP 0205:056, 2002 (arXiv:hep-th/0205185)

• Keshav Dasgupta, Mohammad Sheikh-Jabbari, Mark Van Raamsdonk, Section 2 of: Matrix Perturbation Theory For M-theory On a PP-Wave, JHEP 0205:056, 2002 (arXiv:hep-th/0205185)

See also

• Mike Duff, T. Inami, Christopher Pope, Ergin Sezgin, Kellogg Stelle, Semiclassical Quantization of the Supermembrane, Nucl.Phys. B297 (1988) 515-538 (spire:247064)

• Daniel Kabat, Washington Taylor, section 2 of: Spherical membranes in Matrix theory, Adv. Theor. Math. Phys. 2: 181-206, 1998 (arXiv:hep-th/9711078)

• Nathan Berkovits, Towards Covariant Quantization of the Supermembrane (arXiv:hep-th/0201151)

• Qiang Jia, On matrix description of D-branes (arXiv:1907.00142)

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

• Olaf Lechtenfeld, Hermann Nicolai, A perturbative expansion scheme for supermembrane and matrix theory (arXiv:2109.00346)

Relation to the string dilaton under double dimensional reduction:

• Krzysztof A. Meissner, Hermann Nicolai, Fundamental Membranes and the String Dilaton, J. High Energ. Phys. 2022 219 (2022) $[$arXiv:2208.05822, doi:10.1007/JHEP09(2022)219$]$