M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory

By Washington Taylor. 2001

343 citations recorded by the source corpus.

This article reviews the matrix model of M theory. M theory is an 11-dimensional quantum theory of gravity that is believed to underlie all superstring theories. M theory is currently the most plausible candidate for a theory of fundamental physics which reconciles gravity and quantum field theory in a realistic fashion. Evidence for M theory is still only circumstantial -- no complete background-independent formulation of the theory exists as yet. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, it has appeared in a different guise as the discrete light-cone quantization of M theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory that reduces to a supersymmetric theory of gravity at low energies. Although its fundamental degrees of freedom are essentially pointlike, higher-dimensional fluctuating objects (branes) arise through the non-Abelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8d4280e61389aef36f1791d4202a7beeca15792e

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Citations in the corpus

Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance (2001, background): “example, [36], [20], [6] and section IIC of [56].”
Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture (2004, background): “The “string theory limit” is then a limit where R− is taken to infinity, keeping p+ fixed, i.e.”
D-Branes, Tachyons, and String Field Theory (2003, methodology): “For reviews of M(atrix) theory and AdS/CFT, see Taylor [15] and Aharonyet.al [16].”
Matrix perturbation theory for M-theory on a PP-wave (2002, background): “Since the work of BFSS, matrix theory has passed numerous tests (for a recent review, see [4]), however an honest quantum mechanical study of the model seems extremely difficult, due to the flat directions in the potential (resulting in the continuous spectrum mentioned earlier), the difficulty of d”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “Similar processes in the (2 + 1)-dimensional version of M(atrix) theory [35] transferring flux between different eigenvalues are also non-perturbative: this is interpreted as momentum transfer in some T-dual circle in the type IIB string [36].”
D-branes and K-theory in 2D topological field theory (2006, background): “In the Matrix theory approach to nonperturbative string theory [3][4] open string field theory, or rather its low-energy Yang-Mills theory, is taken to be the fundamental starting point for the formulation of the entire string theory.”
Nonperturbative aspects of ABJM theory (2011, background): “The other terms, with powers which are not multiples of 9, are usually interpreted as “quantum gravity” corrections (see for example the discussion in [22], IV.”