A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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:

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

See Also:

On experimental status

The future of supersymmetry

What if the LHC doesn't see SUSY?

What if LHC finds SUSY?

SUSY and the Large hadron collider


Obtaining supergravity from gauging global supersymmetry

Do commutation relations exist between superfields?

M(atrix) theory and things other than D0-branes? And is it non-peturbative M-theory or non-peturbative Type IIA theory?

Is there an open oriented superstring?

SUSY (Supersymmetric) Quantum Mechanics

What really are exotic supersymmetric black holes?

Quantum master equation in the Batalin-Vilkovisky formalism

Why does in string theory the amount of supersymmetry have to be $\cal{N} \leq 2 $?

supersymmetric Noether theorem and supercurrents -- invariance requirements

Superfields and the Inconsistency of regularization by dimensional reduction

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