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BFSS matrix model

Contents

Contents

Idea

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 NN 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:

  1. as the worldvolume theory of a large number of D0-branes in type IIA string theory,

  2. as the Kaluza-Klein compactification of 10d super Yang-Mills theory to zero space dimensions,

  3. 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.

References

General

The original articles are

Review includes

A review of further developments is in

  • David Berenstein, Classical dynamics and thermalization in holographic matrix models, talk at Leiden, October 2012 (pdf)

Derivation from open string field theory is discussed in

Further perspective includes

Numerical computation:

  • Veselin G. Filev, Denjoe O’Connor, The BFSS model on the lattice, JHEP 1605 (2016) 167 (arXiv:1506.01366)

Relation to the 6d (2,0)-supersymmetric QFT:

Relation to super-membranes

The interpretation of the BFSS model as a regularized M2-brane worldvolume theory is discussed in

Graviton scattering

Computation of graviton scattering amplitudes:

Black holes

Relation to black holes in string theory:

Last revised on September 8, 2018 at 11:10:50. See the history of this page for a list of all contributions to it.