Gravitinos and hidden Supersymmetry at the LHC - Universität ...

Chapter 2
Supersymmetry and Supergravity
Supersymmetry (SUSY) [80–84] is a hypothetical symmetry between fermionic and bosonic
degrees of freedom of a quantum field theory. It introduces fermionic charges transforming
fermions into bosons and vice-versa:
Q |boson〉 ≃ |fermion〉 , Q |fermion〉 ≃ |boson〉 . (2.1)
At first sight, these transformations seem to be similar to internal global symmetry transformations,
for example to isospin, which relates protons and neutrons. Global internal
symmetries lead to conserved charges and superselection sectors within the Hilbert space of
states, cf. [85] and references therein. In this sense they are physical opposed to local gauge
transformations which represent redundancies in the description of the system. Internal global
symmetries have a unifying role, since the states have to be arranged in definite representations
of the considered symmetry group, and these representations can be seen as the basic
ontological objects, as long as the symmetry is unbroken. In the case of isospin, this view
would imply that the true existing objects are nucleon doublets. Proton and neutron appear
as individual objects due to the breaking of isospin by electromagnetic interactions.
The most prominent physical symmetries are the external symmetries of space-time.
Therefore, it would be natural to obliterate the distinction between internal and external
symmetries by combining the global symmetry group with the Lorentz group into some simple
(non-compact) symmetry group. However, it is impossible to accomplish this project as
it was shown by Coleman and Mandula [86].
Here the interesting nature of supersymmetry comes into play, as it turns out that supersymmetry
is the only possible extension of the Poincaré algebra [87], and hence unifies
the boson-fermion relation with the symmetries of space-time. This distinctive nature of supersymmetry
makes it theoretically attractive, irrespective of the possible phenomenological
implications [88]. Unbroken SUSY would imply the existence of mass-degenerate bosons for
each fermion of the Standard Model and vice versa, since it is impossible to combine known
fermions and bosons into supermultiplets, see [89] for a historical overview and references.
Since no such particles were discovered so far, SUSY must be broken.
Nevertheless, SUSY is the most studied extension of the Standard Model and it is expected
to find at least parts of the new particle spectrum of the SM superpartners at the LHC. A
possible attempt for the classification of arguments in favor of the existence of supersymmetry
in nature and for the connection between SUSY and the Fermi-scale can proceed as follows:
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