The BFSS matrix model (Banks-Fischler-Shenker-Susskind 96, Seiberg 97) is the description of the worldline dynamics of interacting D0-branes. In the limit of large number $N$ of D0 branes supposed to encode the strong coupling limit of type IIA string theory (see also at M-theory).
The BFSS matrix model was argued to arise in several equivalent ways:
as the worldvolume theory of a large number of D0-branes in type IIA string theory,
as the Kaluza-Klein compactification of 10d super Yang-Mills theory to zero space dimensions,
as a certain non-commutative regularization of the worldvolume theory of the M2-brane in M-theory (Nicolai-Helling 98, Dasgupta-Nicolai-Plefka 02).
In any case, it ends up being a quantum mechanical system whose degrees of freedom are a set of 9+1 large matrices. These play the role of would-be coordinate functions and their eigenvalues may be in interpreted as points in a spacetime thus defined.
In the 90s there was much excitement about the BFSS model, as people hoped it might provide a definition of M-theory. It is from these times that Edward Witten changed the original suggestion that “M” is for “magic, mystery and membrane” to the suggestion that it is for “magic, mystery and matrix”. (See Witten’s 2014 Kyoto prize speach, last paragraph).
There is also the IKKT matrix model, which takes this one step further by reducing one dimension further down (D(-1)-branes). See also at membrane matrix model.
The original articles are
Tom Banks, Willy Fischler, S.H. Shenker and Leonard Susskind, M Theory As A Matrix Model: A Conjecture Phys. Rev. D55 (1997). (arXiv:hep-th/9610043)
Ashoke Sen, D0 Branes on $T^n$ and Matrix Theory, Adv.Theor.Math.Phys.2:51-59, 1998 (arXiv:hep-th/9709220)
Nathan Seiberg, Why is the Matrix Model Correct?, Phys.Rev.Lett.79:3577-3580, 1997 (arXiv:hep-th/9710009)
Review includes
Tom Banks, Matrix Theory, Nucl.Phys.Proc.Suppl. 67 (1998) 180-224 (arXiv:hep-th/9710231)
Washington Taylor, M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory, Rev.Mod.Phys.73:419-462,2001 (arXiv:hep-th/0101126)
A review of further developments is in
Derivation from open string field theory is discussed in
Further perspective includes
Numerical computation:
Relation to the 6d (2,0)-supersymmetric QFT:
The interpretation of the BFSS model as a regularized M2-brane worldvolume theory is discussed in
Hermann Nicolai, Robert Helling, Supermembranes and M(atrix) Theory, In Trieste 1998, Nonperturbative aspects of strings, branes and supersymmetry 29-74 (arXiv:hep-th/9809103, spire:476366)
Arundhati Dasgupta, Hermann Nicolai, Jan Plefka, An Introduction to the Quantum Supermembrane, Grav.Cosmol.8:1,2002; Rev.Mex.Fis.49S1:1-10, 2003 (arXiv:hep-th/0201182)
Computation of graviton scattering amplitudes:
Katrin Becker, Melanie Becker, A Two-Loop Test of M(atrix) Theory, Nucl.Phys. B506 (1997) 48-60 (arXiv:hep-th/9705091)
Katrin Becker, Melanie Becker, Joseph Polchinski, Arkady Tseytlin, Higher Order Graviton Scattering in M(atrix) Theory, Phys.Rev.D56:3174-3178,1997 (arXiv:hep-th/9706072)
also Kabat-Taylor 97
M. Fabbrichesi, Graviton scattering in matrix theory and supergravity, in: Ceresole A., Kounnas C., Dieter Lüst, Stefan Theisen (eds.) Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Lecture Notes in Physics, vol 525. Springer, Berlin, Heidelberg (arXiv:hep-th/9811204)
Robert Helling, Jan Plefka, Marco Serone, Andrew Waldron, Three-graviton scattering in M-theory, Nuclear Physics B Volume 559, Issues 1–2, 18 October 1999, Pages 184-204 (arXiv:hep-th/9905183)
Robert Echols, M-theory, supergravity and the matrix model: Graviton scattering and non-renormalization theorems, PhD thesis, 1999 pdf
Relation to black holes in string theory:
Tom Banks, Willy Fischler, Igor Klebanov, Leonard Susskind, Schwarzschild Black Holes from Matrix Theory, Phys.Rev.Lett.80:226-229,1998 (arXiv:hep-th/9709091)
Tom Banks, Willy Fischler, Igor Klebanov, Leonard Susskind, Schwarzchild Black Holes in Matrix Theory II, JHEP 9801:008,1998 (arXiv:hep-th/9711005)
Igor Klebanov, Leonard Susskind, Schwarzschild Black Holes in Various Dimensions from Matrix Theory, Phys.Lett.B416:62-66,1998 (arXiv:hep-th/9709108)
Edi Halyo, Six Dimensional Schwarzschild Black Holes in M(atrix) Theory (arXiv:hep-th/9709225)
Gary Horowitz, Emil Martinec, Comments on Black Holes in Matrix Theory, Phys. Rev. D 57, 4935 (1998) (arXiv:hep-th/9710217)
Daniel Kabat, Washington Taylor, Spherical membranes in Matrix theory, Adv.Theor.Math.Phys.2:181-206,1998 (arXiv:hep-th/9711078)
Yoshifumi Hyakutake, Black Hole and Fuzzy Objects in BFSS Matrix Model (arXiv:1801.07869)
Last revised on November 11, 2018 at 08:51:05. See the history of this page for a list of all contributions to it.