Minimal Supersymmetric Standard Model

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 Landscape Minimal Supersymmetric Standard Model String Phenomenology

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Minimal Supersymmetric Standard Model (MSSM)

Superpotential

Following equation 6.1.1 in Martin 1997 (see below).

$W_{MSSM}={\bar {u}}\mathbf {y_{u}} QH_{u}-{\bar {d}}\mathbf {y_{d}} QH_{d}-{\bar {e}}\mathbf {y_{e}} LH_{d}+\mu H_{u}H_{d}$

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 MSSM

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 Theory

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 links

• "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