String Theory
All Roads Lead to String Theory (Polchinski)
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
Superstring Revolutions
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
Horava-Witten String Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

BFSS Matrix Theory, also known as M(atrix) Theory is a fully non-peturbative formulation of M-Theory. It was proposed by Banks, Fischler, Shenker, and Susskind in 1996 [1] .

M(atrix) Theory relies on the AdS/CFT Correspondence, specifically, that

M-Theory in Anti-de-Sitter Space is equivalent to the $ N\to\infty $ limit of Supersymmetryic Quantum Yang-Mills Theory describing D0 branes (point particles).

Here, $ N $ is the dimension of the gauge group $ U(N) $ of the supersymmetric quantum Yang-Mills Theory.

Lagrangian DensityEdit this section

The Lagrangian Density of M(atrix) Theory can immediately be deduced to be the same as in Supersymmetryic Quantum Yang-Mills Theory (N=4 Super-Yang-Mills Theory):

$ \mathsf{\mathcal{L}}=\frac{1}{2{{g}_{s}}\ell _{P}^{2}}\left( \left( \operatorname{tr}\frac{\text{d}{{X}^{\mu }}}{\text{d}\tau } \right)\frac{\text{d}{{X}^{\mu }}}{\text{d}\tau }+2\psi _{\mu }^{{}}\frac{\text{d}\psi _{\mu }^{{}}}{\text{d}\tau }-\frac{1}{2}{{\left( \operatorname{tr}\left[ {{X}^{\mu }},{{X}^{\nu }} \right] \right)}^{2}}-2\psi _{\mu }^{{}}{{\gamma }_{\mu }}\left[ \psi _{{}}^{\mu },{{X}^{\mu }} \right] \right) $

It can be shown [1] that this gives rise to many expected properties of M-Theory, such as brane tension, and $ \mathcal{N}=8 $ Supersymmetry.

ReferencesEdit this section

  1. 1.0 1.1 Banks, Tom; Ficshler, Willy., Shenker, Stephen., Susskind, Leonard. (1996). "M Theory as a Matrix Model: A Conjecture". Physical Review D.```~~~```. 1997 55 (8): 5112-5228. doi:10.1103/PhysRevD.55.5112.