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Cribiori, Niccolò (2018) Non-linear realisations in global and local supersymmetry. [Ph.D. thesis]

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Abstract (italian or english)

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.

Abstract (a different language)

Nella fisica moderna le simmetrie ricoprono un ruolo centrale e, anche nel caso in cui esso sono rotte, possono comunque porre vincoli sulle interazioni. Quando si considerano descrizioni effettive di certi modelli fisici, il gruppo di simmetria può essere infatti spontaneamente rotto ad un suo sottogruppo, ma è comunque possibile scrivere trasformazioni di simmetria che lascino l'azione invariata. Queste trasformazioni sono realizzate non linearmente sui campi, mentre nel regime senza rottura esse agiscono linearmente.

Il Modello Standard della fisica delle particelle può essere interpretato come una teoria effettiva. A tal proposito, sono stati proposti scenari, detti "oltre il Modello Standard", dei quali la supersimmetria è fra i più solidi. Non essendo stata ancora rivelata direttamente negli esperimenti, la supersimmetria è postulata essere spontaneamente rotta ad una certa scala di energia maggiore del TeV. Per questa ragione è importante studiare meccanismi di rottura spontanea di supersimmetria e considerare teorie effettive a bassa energia in cui essa sia realizzata non linearmente. Un ingrediente essenziale di tale classe di modelli è la presenza nello spettro di un fermione di Goldstone a massa nulla, chiamato goldstino, associato ad ogni generatore di supersimmetria spontaneamente rotto.

L'argomento di questa tesi è la costruzione e lo studio di teorie effettive in quattro dimensioni in cui la supersimmetria è spontaneamente rotta e realizzata non linearmente. Nella prima parte viene analizzato il caso di supersimmetria globale. La discussione ha inizio in supersimmetria minimale dal settore di rottura, che descrive il goldstino e le sue interazioni, ed è poi generalizzata ad un numero generico di generatori di supersimmetria spontaneamente rotti.
Viene fornita in particolare una procedura sistematica per costruire teorie effettive con supersimmetria realizzata non linearmente e con qualsiasi contenuto di particelle nello spettro.
Nella seconda parte della tesi, le realizzazioni non lineari sono analizzate nel caso di supersimmetria locale, ovvero supergravità. L'accoppiamento del goldstino alla gravità è presentato inizialmente e, successivamente, il meccanismo di superhiggs è discusso su un generico spazio curvo. Accoppiamenti a materia sono costruiti fornendo alcuni semplici esempi. Una nuova classe di modelli viene poi introdotta, nei quali la supersimmetria è realizzata non linearmente anche nel settore della gravità. Di conseguenza, è possibile costruire azioni nelle quali la costante cosmologica è vincolata ad essere positiva, che possono essere motivate per lo studio di modelli di inflazione.
Due applicazioni delle realizzazioni non lineari in supersimmetria locale sono discusse in dettaglio. Nella prima viene mostrato come implementare l'invarianza di Kaehler in modo che essa funzioni come nel caso di supersimmetria globale. In particolare, la restrizione di tipo Kaehler-Hodge a cui la varietà degli scalari in supergravità deve essere sottoposta, è rilassata. Nella seconda applicazione viene discusso il ruolo delle realizzazioni non lineari nella costruzione di vuoti di tipo de Sitter. L'attenzione è rivolta alla relazione con modelli noti e con un nuovo tipo di D termine in supergravità, proposto recentemente.

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EPrint type:Ph.D. thesis
Tutor:Dall'Agata, Gianguido
Ph.D. course:Ciclo 31 > Corsi 31 > FISICA
Data di deposito della tesi:29 November 2018
Anno di Pubblicazione:30 September 2018
Key Words:Supersymmetry, Supergravity, Supersymmetry breaking, Superfields, Constraints, D-terms
Settori scientifico-disciplinari MIUR:Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Struttura di riferimento:Dipartimenti > Dipartimento di Fisica e Astronomia "Galileo Galilei"
Codice ID:11495
Depositato il:08 Nov 2019 11:13
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