Wess Zumino model in two dimensions

In summary, a Wess Zumino model in two dimensions has real spinors with two components due to the Majorana condition. The superfield is described by A, ψ, and F, which are scalars and a spinorial field, respectively. The supersymmetry generator is given by Q_{\alpha}=\frac{\partial}{\partial \bar{\theta}^{\alpha}} -i \left(\gamma^{\mu} \right) _{\alpha} \partial_{\mu}. The supersymmetry transformations for the fields are A', ψ', and F'. The invariant action of the model is given by S= \int d^{2}x \left[ \frac{1}{2} \
  • #1
alialice
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Homework Statement



Hi!
I need some help to describe a Wess Zumino model in two dimensions:
spinors are real (because of the Majorana condition [itex]\theta=\theta^{\ast}[/itex]) and have two components;
the superfield is:
[itex] \phi \left( x,\theta\right)=A\left( x\right) + i\bar{\theta}\psi\left(x\right) +\frac{i}{2} \bar{\theta}\theta F\left(x\right)[/itex]
where:
A and F are scalars
ψ is a spinorial field.
The susy generator is:
[itex]Q_{\alpha}=\frac{\partial}{\partial \bar{\theta}^{\alpha}} -i \left(\gamma^{\mu} \right) _{\alpha} \partial_{\mu}[/itex]

1) What are the supersymmetry transformations of the fields?

2) Which is the invariant action of the model?

Thank you very much if you could give me some help!
 
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  • #2
Homework Equations N/AThe Attempt at a Solution 1) The supersymmetry transformations of the fields are:A: A'\left(x\right)= A\left(x\right)+ i\bar{\epsilon}\psi\left(x\right) ψ: ψ'\left(x\right)= ψ\left(x\right)+ i\epsilon F\left(x\right) F: F'\left(x\right)= F\left(x\right)+ i\bar{\epsilon}\gamma^{\mu}\partial_{\mu}\psi\left(x\right) 2) The invariant action of the model is:S= \int d^{2}x \left[ \frac{1}{2} \partial^{\mu}A \partial_{\mu}A + \frac{i}{2}\bar{\psi}\gamma^{\mu}\partial_{\mu}\psi + \frac{1}{2}F^{2} \right]
 

1. What is the Wess Zumino model in two dimensions?

The Wess Zumino model in two dimensions is a quantum field theory that describes the interactions between fermions and bosons in two-dimensional space. It is a supersymmetric extension of the two-dimensional nonlinear sigma model.

2. What are the main features of the Wess Zumino model?

The Wess Zumino model has several key features, including supersymmetry, which relates fermions and bosons, and chiral symmetry, which relates left-handed and right-handed fields. It also has a nonrenormalizable coupling, which requires the introduction of a cutoff scale.

3. What is the significance of the Wess Zumino term in the model?

The Wess Zumino term is a topological term that is added to the Lagrangian of the model. It is important because it is responsible for the anomaly cancellation in the model, which ensures that quantum corrections do not destroy the symmetries of the theory.

4. How is the Wess Zumino model related to supersymmetry breaking?

The Wess Zumino model is a supersymmetric theory, so it is often used as a starting point for studying supersymmetry breaking. By adding a supersymmetry breaking term to the Lagrangian, the model can be used to explore different mechanisms for breaking supersymmetry and its implications.

5. What are some applications of the Wess Zumino model in two dimensions?

The Wess Zumino model has been used in various fields of theoretical physics, including string theory and condensed matter physics. It has also been applied to the study of supersymmetric gauge theories and the AdS/CFT correspondence. Additionally, the model has been used to investigate the role of supersymmetry in the early universe and in particle physics beyond the Standard Model.

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