Geometric structure of generalised gauge field theories

doctoral thesis

• Title (croatian): Geometrijska struktura teorija polja s poopćenim baždarnim simetrijama
• Author: Clay James Grewcoe
• Mentor: Larisa Jonke (mentor)
• Committee member: Athanasios Chatzistavrakidis (predsjednik povjerenstva)
• Committee member: Larisa Jonke (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2021-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics
• Universal decimal classification (UDC): 53 - Physics

Abstract

Generalised gauge field theories are interacting field theories with a gauge symmetry generalised beyond the standard Lie algebra case. Such theories have become increasingly important in modern physics, especially high energy physics as the search for a consistent description of quantum gravity makes these generalised symmetries unavoidable. Two theories we shall analyse in particular are the Courant sigma model and double field theory. They are relevant in the understanding of dualities and symmetries with higher form gauge fields. The aim of this thesis is to explore deeper the relation between the two and to embed them into the appropriate framework for studying higher gauge symmetries – L∞-algebras. This will be broken down into three parts. The first dedicated to delving deeper into the BRST symmetry of them and exploring how the known classical projection procedure relating them appears on the BRST level. It is at this point that we explicitly see the necessity of the strong constraint for double field theory to be covariant. Having understood the BRST structure and knowing that the Courant algebroid, the geometric structure behind the sigma model, is an L∞-algebra we are motivated to see how the full field theory fits into this framework. This is the second part. In it we construct the L∞-algebra for the Courant sigma model in such a way that all physical data can be expressed using the objects and operations defined by the algebra itself. Then the intimate relationship between L∞ and the Batalin-Vilkovisky formalism is utilised to obtain its BV/BRST formulation. Finally, in the last part, we go back to double field theory and embed its geometric structure, the DFT algebroid, into L∞ much the same way as the Courant algebroid is. However, because of the section condition of double field theory this cannot be done as is, given that the cohomological vector in this formulation squares to zero only upon applying the section condition. In order to get around this we turn to the well known but extremely rarely used extension of L∞-algebras – curved L∞-algebras. It is precisely this curving that encapsulates the strong constraint violating terms and restores the existence of the cohomological vector. We finish off with a sigma model built upon this new curved algebra that brings about the section condition as an on-shell requirement.

Abstract (croatian)

Rad ne sadrži sažetak na drugom jeziku.

• Keywords: L∞-algebra; Batalin-Vilkovisky; double field theory; gauge symmetry; courant algebroid
• Keywords (croatian): L∞-algebra; Batalin-Vilkovisky; dvostruka teorija polja; baždarna simetrija; Courantov algebroid
• Language: english
• URN:NBN: urn:nbn:hr:217:474161
• Promotion: 2021
• Study programme: Title: Physics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika (doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika)
• Type of resource: Text
• Extent: X, 121 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-07-23 10:12:28