Abstract
dc:description.abstract<p>The infinite-dimensional symmetry algebra of a conformal field theory (CFT), the Virasoro algebra, is generated by the holomorphic and anti-holomorphic part of the stress tensor. Besides such 'chiral symmetries' the CFT also has an integrable symmetry, that is, infinite families of commuting conserved charges. In this thesis a step towards combining these two symmetries into a single formalism is taken, by identifying integrable stuctures of a CFT through studying the representation category of the underlying chiral algebra. Then by introducing defects in the system, conserved charges can be constructed by perturbing certain conformal defects.<br/> Starting from an abelian rigid braided monoidal category C one defines an abelian rigid monoidal category C<sub>F</sub> which captures some aspects of perturbed conformal defects in two-dimensional CFT. Namely, for V a rational vertex operator algebra one considers the charge-conjugation CFT constructed from V (the Cardy case). Then C = <strong>Rep</strong>(V) and an object in C<sub>F</sub> corresponds to a conformal defect condition together with a direction of perturbation. To each object in C<sub>F</sub> one assigns a perturbed defect operator on the space of states of the CFT and then shows that the assignment factors through the Grothendieck ring of C<sub>F</sub>. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.</p>
Degree
thesis:*- Name dc:type.qualificationname
- Doctor of Philosophy
- Level dc:type.qualificationlevel
- Doctoral Thesis
- Grantor dc:publisher.institution
- King's College London
- Year dc:date.issued
- 2012
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Manolopoulos, Dimitris
- Advisors dc:contributor.advisor
-
- Watts, Gerard Marcel Tannerie
- Runkel, Ingo
- Recknagel, Andreas Harry
Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- oai:kclpure.kcl.ac.uk:studenttheses/23890e88-b5cf-4c59-910a-5ed4d8f8acfc
- OAI identifier oai:identifier
- oai:kclpure.kcl.ac.uk:studenttheses/23890e88-b5cf-4c59-910a-5ed4d8f8acfc