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On the Killing form of Lie Algebras in Symmetric Ribbon Categories
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik (from 2013).
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik (from 2013).ORCID-id: 0000-0003-4081-6234
2015 (engelsk)Inngår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 11, artikkel-id 017Artikkel i tidsskrift (Fagfellevurdert) Published
Resurstyp
Text
Abstract [en]

As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.

sted, utgiver, år, opplag, sider
NATL ACAD SCI UKRAINE , 2015. Vol. 11, artikkel-id 017
Emneord [en]
Lie algebra, monoidal category, Killing form, Lie superalgebra
HSV kategori
Forskningsprogram
Fysik
Identifikatorer
URN: urn:nbn:se:kau:diva-41659DOI: 10.3842/SIGMA.2015.017ISI: 000350561700001OAI: oai:DiVA.org:kau-41659DiVA, id: diva2:918428
Tilgjengelig fra: 2016-04-11 Laget: 2016-04-11 Sist oppdatert: 2019-12-09bibliografisk kontrollert
Inngår i avhandling
1. Strings, Gravitons, and Effective Field Theories
Åpne denne publikasjonen i ny fane eller vindu >>Strings, Gravitons, and Effective Field Theories
2016 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes.

Abstract [en]

Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory.

With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

sted, utgiver, år, opplag, sider
Karlstad: Karlstads universitet, 2016. s. 57
Serie
Karlstad University Studies, ISSN 1403-8099 ; 2016:30
Emneord
string theory, amplitudes, supersymmetry, particle phenomenology, BMSSM, modified gravity, bimetric, massive gravity, Lie algebras, ribbon categories
HSV kategori
Forskningsprogram
Fysik
Identifikatorer
urn:nbn:se:kau:diva-41912 (URN)978-91-7063-708-7 (ISBN)
Disputas
2016-06-03, 21A342, Karlstad University, Karlstad, 13:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2016-05-13 Laget: 2016-04-25 Sist oppdatert: 2016-05-13bibliografisk kontrollert

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