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Title: Supersymmetry algebras in arbitrary dimension and signature
Author: Gall, Louis
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2019
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In this thesis, a formalism is presented that allows the construction of supersymmetry algebras in arbitrary dimension in such a way that the space-time SO(t,s) and R-symmetry transformations are disentangled completely (for odd dimensions) or almost completely (in even dimensions). This is done by first taking multiple copies of the underlying spinor representation and defining complex bilinear superbrackets on the resulting space. Real supersymmetry algebras are then obtained by imposing signature-dependent reality conditions. This construction generalises and includes symplectic Majorana spinors. For dimensions up to twelve, we classify all supersymmetry algebras of any space-time signature whose R-symmetry groups are real forms of the R-symmetry group of complex superbrackets based on charge conjugation matrices. While not providing a full classification up to isomorphism, this method allows one to identify cases where more than one supersymmetry algebra exists for a given signature with any number of supercharges. In particular, for Lorentz signature, we find alternative 'type-*' or 'twisted' superalgebras with non-compact R-symmetry groups. This formalism is then applied to five- and four-dimensional N = 2 supersymmetry algebras and is used to derive vector multiplet theories in any signature. In five dimensions, the physical Lagrangians and supersymmetry representations are found by imposing signature-dependent reality conditions on a holomorphic master Lagrangian and associated supersymmetry variations to obtain signature-dependent theories. Fourdimensional Lagrangians are found through the dimensional reduction of these Lagrangian and supersymmetry representations. In four-dimensional Minkowski signature the existence of a 'twisted' supersymmetry algebra with U(1,1) R-symmetry is demonstrated and the vector multiplet theory derived from this algebra is shown to necessarily have ghost fields. Additionally, an alternative classification of the N = 1 and N = 2 supersymmetry algebras is performed in five and four dimensions following the method of [1], classifying the possible superalgebras in each signature up to isomorphism. In five dimensions there is a one-parameter family of superalgebras, and in four dimensions the space of superbrackets is found to have the same structure as the associated space-time R t,s.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral