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 <math>\begin{align}   & \left\{ \begin{align}   & m{\alpha }'\tau \hbar \varepsilon \mu \alpha \mathbf{T}ic\varsigma  \\   & \text{      }\And  \\   & \text{  }\mathsf{\mathcal{P}}\pi y\sigma \mathbf{I}\subset \mathbf{S} \\  \end{align} \right\} \\   & \text{    }Wikia \\  \end{align}</math>

Minimal Supersymmetric Standard Model

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String Theory
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All Roads Lead to String Theory (Polchinski)
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
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Minimal Supersymmetric Standard Model
String Phenomenology



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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.

External linksEdit this section

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