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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
| SupersymmetryRNS 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 | |

**Supersymmetry** (SUSY) A postulated symmetry between bosonic and fermionic fields in Quantum Field Theoryies and String Theoryies.

The theory of Supsersymmetry has been incorporated in the Standard Model (MSSM), Yang-Mills Theory (Super-Yang-Mills Theory), and most famously String Theory (Superstring theory).

While **Supersymmetry** remains experimentally unconfirmed, one of its greatest achievements is that the MSSM (which also appears in realistic M-Theory vacua) predicts a Higgs of mass 125 GeV (which was measured by the LHC recently.), which is contrary to the Standard Model, which predicts such a mass to be rather unlikely.

## Technical detailsEdit this section

There are two types of **supersymmetry**; worldsheet supersymmetry, and spacetime supersymmetry.

### Worldsheet supersymmetryEdit this section

The RNS Formalism has explicit worldsheet supersymmetry. Since the RNS Action is given by adding the Polyakov Action to the Dirac Action, it is given by:

$ {{\mathsf{\mathcal{L}}}_ {RNS}}=\frac{T}{2} h^{\alpha \beta} \left( \partial_\alpha X^\mu \partial_\beta X^\nu +i\hbar c_0 \bar{\psi_\mu} \not{\partial} \psi^\mu \right) g_{\mu\nu} $

The **supersymmetryic** transformations on the worldsheet can therefore be (almost trivially, by taking variations of this above action) shown to be:

$ \begin{align} \delta {X^\mu } \to \bar \epsilon {\psi ^\mu } ; \\ \delta {\psi ^\mu } \to - i \not \partial {X^\mu }\epsilon \\ \end{align} $

### Spacetime SupersymmetryEdit this section

The GS Formalism, or the Superspace Formalism, are with explicit spacetime **supersymmetry**. The **supersymmetryic** transformations on spacetime are (which is rather intuitive if you compare this to the RNS Worldsheet supersymmetry transformations) given by:

$ \begin{align} \delta {\Theta ^{Aa}} \leftrightarrow {\varepsilon ^{Aa}} ; \\ \delta {X^\mu } \leftrightarrow {{\bar \varepsilon }^A}{\gamma ^\mu }{\Theta ^A} \\ \end{align} $