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Linking Chains Together: String Bits and the Bethe Ansatz
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS5 x S5 and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS5 rotate quickly around the equator of the S5 and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order.

Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers from the problem of fermion doubling, a general pathology of fermions on a lattice. In paper II we show how to adjust the theory in order to avoid this problem and, in fact, use the fermion doubling to our advantage. The second part of the thesis studies the low energy behaviour of SU(2) Yang-Mills theory in 4 space-time dimensions. In paper I we perform numerical calculations on an effective action for this theory. We propose the existence of a knotted trajectory within the dynamics of this effective action.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2004. , p. 70
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 1047
Keywords [en]
Theoretical physics, theoretical physics, string theory, string bit, Bethe ansatz
Keywords [sv]
Teoretisk fysik
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-4691ISBN: 91-554-6108-5 (print)OAI: oai:DiVA.org:uu-4691DiVA, id: diva2:165509
Public defence
2004-12-14, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15
Opponent
Supervisors
Available from: 2004-11-22 Created: 2004-11-22Bibliographically approved
List of papers
1. Asymptotically free Yang-Mills classical mechanics with selflinked orbits
Open this publication in new window or tab >>Asymptotically free Yang-Mills classical mechanics with selflinked orbits
2003 In: Physics Letters B, ISSN 0370-2693, Vol. 568, p. 176-180Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-92431 (URN)
Available from: 2004-11-22 Created: 2004-11-22Bibliographically approved
2. String bits without doubling
Open this publication in new window or tab >>String bits without doubling
2003 In: Journal of High Energy Physics, ISSN 1029-8479, Vol. 10, no 026Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-92432 (URN)
Available from: 2004-11-22 Created: 2004-11-22Bibliographically approved
3. Finite-size corrections to anomalous dimensions in N=4 SYM theory
Open this publication in new window or tab >>Finite-size corrections to anomalous dimensions in N=4 SYM theory
2004 In: Journal of High Energy Physics, ISSN 1029-8479, Vol. 05, no 049Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-92433 (URN)
Available from: 2004-11-22 Created: 2004-11-22Bibliographically approved

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