# Minimal Supersymmetric Standard Model

*118*articles on

the Psi Epsilon Wikia

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 String Bosonic String Theory String Perturbation Theory Tachyon Condensation | |

Supersymmetric Revolution
| Supersymmetry RNS Formalism GS Formalism BPS | |

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 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
| ||

Phenomenology
| String Theory LandscapeMinimal Supersymmetric Standard ModelString Phenomenology | |

This |

**Minimal Supersymmetric Standard Model** (MSSM)

## SuperpotentialEdit this section

Following equation 6.1.1 in Martin 1997 (see below).

where are superfields ( the up-type Higgs, the down-type Higgs, a left-handed quark multiplet, a left-handed lepton multiplet, and right-handed quark superfields, right-handed charged-lepton superfield), and is the 3x3 matrix of yukawa couplings for fermions of type . (Superfields actually have subscripts running from 1 to 3, so each yukawa term in the superpotential above is actually a sum over generations, but subscripts have been neglected here.)

## Variations on the MSSMEdit this section

CMSSM (constrained MSSM) - has just 5 parameters.

pMSSM (phenomenological MSSM) - has 19 parameters.

NMSSM (next-to-minimal SSM) - has an extra scalar field.

G2-MSSM - region of MSSM parameter space which Kane, Acharya, and Kumar argue is characteristic of M-Theory compactified on G2 Manifolds (see below).

## MSSM from String TheoryEdit this section

In String Phenomenology, the MSSM may be produced from a string vacuum whose field-theory limit is an supersymmetric Grand Unified Theory (GUT).

For example, Anderson, Lukas, Gray, Palti (2011) constructed 208 "heterotic standard models" in which the field-theory limit is a type of GUT that is then broken to the MSSM.

In principle, each such vacuum will give rise to MSSM with particular parameter settings (for coupling constants, yukawa couplings, etc.), which can then be tested against experiment. But in practice, it is still very difficult to determine the parameter values that arise from a particular vacuum, and progress towards testability is slow.

This sort of String Phenomenology is useful for String Theory, as it is important for string vacua to give rise to the MSSM at the field-theory limit. For example, Kumar, Acharya, and Kane showed in 2010 that some realistic vacua of M-Theory give rise to the MSSM suitably.

## External linksEdit this section

- "A Supersymmetry Primer" (Stephen Martin) is a well-known introduction to the MSSM
- Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds (Anderson, Lukas, Gray, Palti)
- Kumar, Kane, Acharya