# Matrix String Theory

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String Theory
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All Roads Lead to String Theory (Polchinski)
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Prior to the First Superstring Revolution
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Early History
| S-Matrix Theory Regge Trajectory | |

Bosonic String Theory
| Worldsheet String Bosonic String Theory String Perturbation Theory Tachyon Condensation | |

Supersymmetric Revolution
| Supersymmetry RNS Formalism GS Formalism BPS | |

Superstring Revolutions
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First Superstring Revolution
| GSO Projection Type II String Theory Type IIB String Theory Type IIA String Theory Type I String Theory Type H String Theory Type HO String Theory Type HE String Theory | |

Second Superstring Revolution
| T-Duality D-Brane S-Duality Horava-Witten String Theory M-Theory Holographic Principle N=4 Super-Yang-Mills Theory AdS CFT BFSS Matrix Theory Matrix String Theory(2,0) Theory Twistor String Theory F-Theory String Field Theory Pure Spinor Formalism | |

After the Revolutions
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Phenomenology
| String Theory Landscape Minimal Supersymmetric Standard Model String Phenomenology | |

**Matrix String Theory** is a non-perturbative formulation of Type IIA String Theory and Type HE String Theory. It was discovered by Lubos Motl in 1997 ^{[1]} ^{[2]} ^{[3]} ^{[4]} ^{[5]} .

## Type IIA Matrix String TheoryEdit this section

Type IIA Matrix String Theory is the Matrix Model formulation of Type IIA String Theory.

The momenta in BFSS Matrix Theory are quantised as /. In BFSS Matrix Theory, . Therefore, the explanation given for this by Motl is that in uncompactified M-Theory, is .

Since when M-Theory is compactified on a light-like circle, this becomes finite, so should , to have a well-defined momenta.

M-Theory compactified on a light-circle is related by a Lorentz Transform to M-Theory compactified on a space-like circle. This is because a Lorentz Transform transforms between space-like coordinates and time-like ones.

The actual Lorentz Transform2 can be calculated as follows:

Type IIA Matrix String Theory still has a gauge group of , but with a finite , .

## Type HE Matrix String TheoryEdit this section

Type HE Matrix String Theory is much more difficult than Type IIA Matrix String Theory, because to have an 11-Dimensional Interpretation (a consistent M-Theory which gives rise to this theory when the=re is a Horava-Witten Boundary), extra fields, called the -fields (also known as the "Chi-Fields"), need to be added. See ^{[1]}. Equation 3.1 of ^{[1]} is basically, as one may see from the Dirac Field Lagrangian Density, that:

Note that the first is not conjugated, because this is unnecessary (the -field is real).

## ReferencesEdit this section

- ↑
^{1.0}^{1.1}^{1.2}Motl, Lubos; Banks, Thomas. (2001). "Nonperturbative Formulations of Superstring Theory".*New Brunswick Rutgers, The State University of New Jersey*. http://arxiv.org/pdf/hep-th/0109149.pdf. - ↑ Motl, Lubos; Susskind, Leonard. (1997). "Finite N Heterotic Matrix Models and Discrete Light Cone Quantization".
*ArXiV*. http://arxiv.org/pdf/hep-th/9708083v2.pdf. - ↑ Motl, Lubos; Banks, Thomas. (1997). "Heterotic Strings from Matrices".
*Journal of High Energy Physics***9712**(4). http://arxiv.org/pdf/hep-th/9703218v1.pdf. - ↑ Motl, Lubos (1997). "Proposals on nonperturbative superstring interactions".
*ArXiV*. http://arxiv.org/pdf/hep-th/9701025v3.pdf. - ↑ Motl, Lubos (1997). "Quaternions and M(atrix) theory in spaces with boundaries".
*ArXiV*. http://arxiv.org/pdf/hep-th/9612198v3.pdf.