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Non-linear realisations of supersymmetry using constrained superfields

Elbers, W.H. (2016) Non-linear realisations of supersymmetry using constrained superfields. Bachelor's Thesis, Physics.

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Abstract

A non-linear group realisation is a homomorphism from a group to a group of transformations of a topological space. Non-linear realisations of symmetry groups are important in physics, where they occur in quantum field theories with spontaneous symmetry breaking. For this reason, one studies the non-linear Volkov-Akulov realisation of supersymmetry in theories with supersymmetry breaking. One popular technique for obtaining the Volkov-Akulov realisation makes use of a linear realisation that is made to satisfy a non-linear constraint. We investigate the validity of this approach. In order to tackle this problem, we prove a number of results concerning non-linear realisations in general. In particular, we show that imposing an algebraic constraint on a (non-)linear realisation yields another non-linear realisation, provided that the constraint itself is invariant under the transformation group. Subsequently, we formally derive linear and non-linear realisations of the superPoincaré group using the notion of smooth superfunctions in superspace. Finally, for a general non-linear sigma model with global supersymmetry and $n$ chiral superfields, we derive conditions on the Kähler and superpotential that guarantee that the goldstino superfield Phi satisfies a given nilpotency condition Phi^k=0 for k=2,3 in the limit of infinite UV cut-off scale and at energies far below the mass of the sgoldstino.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Physics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:24
Last Modified: 15 Feb 2018 08:24
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/14443

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