|All Roads Lead to String Theory (Polchinski)|
Prior to the First Superstring Revolution
|Early History|| S-Matrix Theory|
|Bosonic String Theory|| Worldsheet|
Bosonic String Theory
String Perturbation Theory
|Supersymmetric Revolution|| Supersymmetry|
|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
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
|Phenomenology|| String Theory Landscape|
Minimal Supersymmetric Standard Model
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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.
MSSM from String TheoryEdit this section
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.
- "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