Abstract
In this chapter, we revisit the simplest globally supersymmetric field theory in four dimensions, the free massless Wess–Zumino model for one chiral multiplet, and discuss how this theory has to be changed when supersymmetry is turned into a local symmetry. As we will see, making supersymmetry local by a simple iterative procedure (the “Noether method”) directly exhibits the need for the gravitino field and its superpartner, the graviton, and suggests the supersymmetry transformation laws of these fields.
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Notes
- 1.
Note that, since we are not using auxiliary fields, the supersymmetry algebra closes only on-shell:
where […] denotes a non-vanishing expression of the fields and supersymmetry parameters. The last term then vanishes due to the field equation
, and one obtains the usual susy algebra \(\left [ \delta _{\epsilon _{2}} , \delta _{\epsilon _{1}} \right ] = \frac 12(\overline {\epsilon }_{1}\gamma ^{\mu }\epsilon _{2})\partial _{\mu }\) on all fields. - 2.
For the sake of readability, we do not distinguish carefully here between spin and helicity, i.e., “spin s” should be understood as “helicity ± s” in the massless case.
- 3.
We will see in Sect. 4.2.2 that in the presence of a (negative) cosmological constant, the concept of mass will be slightly different from the one we are used to in the flat case.
, and one obtains the usual susy algebra References
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Dall’Agata, G., Zagermann, M. (2021). From Global to Local Supersymmetry. In: Supergravity. Lecture Notes in Physics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-63980-1_2
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DOI: https://doi.org/10.1007/978-3-662-63980-1_2
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