Non-linear realisations in global and local supersymmetry

In modern physics the role of symmetries is central and, even when they are broken, their remnants can pose constraints on the interactions. In considering effective descriptions of certain physical models, the symmetry group can be indeed spontaneously broken to some subgroup, but it is still possible to write symmetry transformations which leave a given action invariant. These transformations are usually realised non-linearly on the fields, while in the unbroken regime they act linearly. The Standard Model of particle physics can be though of as an effective theory. In this respect, beyond the Standard Model scenarios have been proposed, of which supersymmetry is one of the best motivated at present. Having been yet no direct detection in the experiments, supersymmetry is postulated to be spontaneously broken at some energy scale above the TeV. For this reason, it is important to study supersymmetry breaking mechanisms and to consider low energy effective theories with spontaneously broken and non-linearly realised supersymmetry.An essential ingredient of this class of models is the presence of a massless goldstone fermion in the spectrum, namely a goldstino, which is associated to each broken generator.The subject of this thesis is the construction and the study of four-dimensional effective theories with spontaneously broken and non-linearly realised global and local supersymmetry. In the first part, the global supersymmetric case is analysed. The discussion starts from the supersymmetry breaking sector, describing the goldstino and its interactions, in the case of minimal supersymmetry and it is then generalised to a generic number of spontaneously broken supersymmetry generators.A systematic procedure is given in order to construct effective theories with non-linearly realised supersymmetry and with any desired spectrum content. In the second part of the thesis, non-linear realisations are analysed in the case of local supersymmetry, namely supergravity. The coupling of the goldstino sector to gravity is presented first and the superhiggs mechanism on a generic background is discussed. Matter couplings are then constructed in some simple examples. A new class of models is introduced in which supersymmetry is spontaneously broken and non-linearly realised already on the gravity sector. As a consequence, it is possible to construct actions in which the cosmological constant is bounded to be positive, which can be motivated for studying inflation. Two applications of non-linear realisations in local supersymmetry are discussed in detail. In the first one it is shown how to implement Kaehler invariance in a way that mimics the global supersymmetric case. In particular, the Kaehler-Hodge restriction on the scalar manifold, which is typical of supergravity, is avoided. In the second application the role of non-linear realisations in the construction of de Sitter vacua is discussed. Attention is devoted to the relationship with known de Sitter uplift constructions and with a new, recently proposed D-term in supergravity.

Note:

152 pages. Ph.D. thesis based on: arXiv:1607.01277, arXiv:1611.01490, arXiv:1704.07387 & arXiv:1712.08601

Supersymmetry
Supergravity
Supersymmetry breaking
Superfields
Constraints
D-terms
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
supersymmetry: local
representation: nonlinear
supersymmetry: spontaneous symmetry breaking

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