## FANDOM

118 Pages

String Theory
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
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 Landscape
Minimal Supersymmetric Standard Model
String Phenomenology

 This article or section is in the midst of a heavy restructuring or expansion process. Feel free to contribute by participating in this process.

Minimal Supersymmetric Standard Model (MSSM)

## SuperpotentialEdit this section

Following equation 6.1.1 in Martin 1997 (see below).

$W_{MSSM} = \bar{u} \mathbf{y_u} Q H_u - \bar{d} \mathbf{y_d} Q H_d - \bar{e} \mathbf{y_e} L H_d + \mu H_u H_d$

where $u, Q, H_u, H_d, L, e$ are superfields ($H_u$ the up-type Higgs, $H_d$ the down-type Higgs, $Q$ a left-handed quark $SU(2)$ multiplet, $L$ a left-handed lepton $SU(2)$ multiplet, $u$ and $d$ right-handed quark superfields, $e$ right-handed charged-lepton superfield), and $y_f$ is the 3x3 matrix of yukawa couplings for fermions of type $f$. (Superfields $u, Q, L, e$ actually have subscripts running from 1 to 3, so each yukawa term in the superpotential above is actually a sum $\Sigma_{ij}$ 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 $\mathcal{N}=1$ 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 $SU(5)$ 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.