Wess Zumino model in two dimentions

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SUMMARY

The discussion centers on the Wess Zumino model in two dimensions, emphasizing the use of real spinors due to the Majorana condition. The superfield is defined as \(\phi\left(x,\theta \right)= A(x) + i \bar{\theta} \psi(x) + \frac{1}{2} i \bar{\theta} \theta F(x)\), where \(A\) and \(F\) are scalar fields and \(\psi\) is a spinorial field. The supersymmetry generator is given by \(Q_{\alpha} = \frac{\partial}{\partial \bar{\theta^{\alpha}}} - i (\gamma_{\mu} \theta )_{\alpha} \partial_{\mu}\). The discussion seeks assistance in determining the supersymmetry transformations of the fields and the invariant action of the model.

PREREQUISITES
  • Understanding of supersymmetry and its mathematical framework
  • Familiarity with Majorana spinors and their properties
  • Knowledge of superfields and their components in quantum field theory
  • Basic concepts of action invariance in field theories
NEXT STEPS
  • Research the derivation of supersymmetry transformations for the Wess Zumino model
  • Study the construction of invariant actions in supersymmetric field theories
  • Explore the implications of Majorana conditions on spinorial fields
  • Examine references on two-dimensional supersymmetry, such as "Supersymmetry and Supergravity" by A. Salam and J. Strathdee
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory and supersymmetry, as well as graduate students seeking to deepen their understanding of the Wess Zumino model.

alialice
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Hi!
I need some help to describe a Wess Zumino model in two dimensions: spinors are real (because of the Majorana condition) and the superfield is:
\phi\left(x,\theta \right)= A(x) + i \bar{\theta} \psi(x) + \frac{1}{2} i \bar{\theta} θ F(x)
where:
A and F are scalar
ψ is a spinorial field
1) What are the supersymmetry transformations of the fields?
The susy generator is:
Q_{\alpha} = \frac{\partial}{\partial \bar{\theta^{\alpha}}} - i (\gamma_{\mu} \theta )_{\alpha} \partial_{\mu}
2) Which is the invariant action of the model?
Thank you very much if you could give me some help! :smile:
 
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or do you know a reference where I can found this?
 
Is there someone who knows how to calculate the susy transformations please?
 

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