# Tag Info

Supersymmetry (SUSY) A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories. In non-technical terms, this means that each bosonic field or particle has a fermionic superpartner and vice versa,. .

The theory of Supsersymmetry has been incorporated in the (), theory (Super-Yang-Mills Theory), and most famously String Theory ().

While Supersymmetry remains experimentally unconfirmed, one of its greatest achievements is that the MSSM (which also appears in realistic vacua) predicts a higgs of mass 125 GeV (which was measured by the LHC recently.), which is contrary to the , which predicts such a mass to be rather unlikely.

# Technical details

There are two types of ; worldsheet supersymmetry, and spacetime supersymmetry

## Worldsheet supersymmetry

The Ramond-Neveu-Schwarz formalism has explicit worldsheet supersymmetry. Since the RNS Action is given by adding the Polyakov Action to the Dirac action, it is given by:

$${{\mathsf{\mathcal{L}}}_ {RNS}}=\frac{T}{2} h^{\alpha \beta} \left( \partial_\alpha X^\mu \partial_\beta X^\nu +i\hbar c_0 \bar{\psi_\mu} \not{\partial} \psi^\mu \right) g_{\mu\nu}$$

The supersymmetric transformations on the worldsheet can therefore be (almost trivially, by taking variations of this above action) shown to be:

$$\begin{gathered} \delta {X^\mu } \to \bar \epsilon {\psi ^\mu } ; \\ \delta {\psi ^\mu } \to - i \not \partial {X^\mu }\epsilon \\ \end{gathered}$$

# Spacetime Supersymmetry

The Green-Schwarz formalism, or the , are with explicit spacetime supersymmetry. The supersymmetric transformations on spacetime are (which is rather intuitive if you compare this to the RNS Worldsheet supersymmetry transformations) given by:

$$\begin{gathered} \delta {\Theta ^{Aa}} \leftrightarrow {\varepsilon ^{Aa}} ; \\ \delta {X^\mu } \leftrightarrow {{\bar \varepsilon }^A}{\gamma ^\mu }{\Theta ^A} ; \\ \end{gathered}$$

## On experimental status

The future of supersymmetry

What if the LHC doesn't see SUSY?

## Others

Do commutation relations exist between superfields?

SUSY (Supersymmetric) Quantum Mechanics

supersymmetric Noether theorem and supercurrents -- invariance requirements