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Aspects of Yang-Mills Theory: Solitons, Dualities and Spin Chains
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties.

Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theory in AdS5×S5 is dual to four dimensional Yang-Mills with four supersymmetries. The duality relate the non perturbative regime of one of the theories to the perturbative regime of the other. This makes it in general hard to test this conjecture. For a special type of solutions it is however possible to use a perturbative expansion in both theories. We discuss this type of solutions and in particular we discuss a method, the Bethe ansatz, to find the solutions on the gauge theory side.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2004. , p. 87
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 1002
Keywords [en]
Theoretical physics, Theoretical Physics, Field theory, String theory, Yang-Mills, Effective models, Supersymmetry, Solitons, Fermion number, Duality, AdS/CFT correspondence, Bethe ansatz
Keywords [sv]
Teoretisk fysik
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-4498ISBN: 91-554-6017-8 (print)OAI: oai:DiVA.org:uu-4498DiVA, id: diva2:164963
Public defence
2004-09-28, Å4001, Ångström laboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15
Opponent
Supervisors
Available from: 2004-09-06 Created: 2004-09-06Bibliographically approved
List of papers
1. Shafranov's virial theorem and magnetic plasma confinement
Open this publication in new window or tab >>Shafranov's virial theorem and magnetic plasma confinement
2002 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 11, p. L133-L139Article in journal, Letter (Refereed) Published
Abstract [en]

Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field, which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-92022 (URN)10.1088/0305-4470/35/11/101 (DOI)
Available from: 2004-09-06 Created: 2004-09-06 Last updated: 2017-12-14Bibliographically approved
2. Field decomposition and the ground state structure of SU(2) Yang-Mills theory
Open this publication in new window or tab >>Field decomposition and the ground state structure of SU(2) Yang-Mills theory
2002 (English)In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 17, no 25, p. 3681-3688Article in journal (Refereed) Published
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-92023 (URN)10.1142/S0217751X02010753 (DOI)
Available from: 2004-09-06 Created: 2004-09-06 Last updated: 2017-12-14Bibliographically approved
3. Chirality and fermion number in a knotted soliton background
Open this publication in new window or tab >>Chirality and fermion number in a knotted soliton background
2003 (English)In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 557, no 1-2, p. 121-124Article in journal (Refereed) Published
Abstract [en]

We consider the coupling of a single Dirac fermion to the three component unit vector field which appears as an order parameter in the Faddeev model. Classically, the coupling is determined by requiring that it preserves a certain local frame independence. But quantum mechanically the separate left- and right-chiral fermion number currents suffer from a frame anomaly. We employ this anomaly to compute the fermion number of a knotted soliton. The result coincides with the self-linking number of the soliton. In particular, the anomaly structure of the fermions relates directly to the inherent chiral properties of the soliton. Our result suggests that interactions between fermions and knotted solitons can lead to phenomena akin the Callan–Rubakov effect.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-92024 (URN)10.1016/S0370-2693(03)00200-4 (DOI)
Available from: 2004-09-06 Created: 2004-09-06 Last updated: 2017-12-14Bibliographically approved
4. The supersymmetric extension of the Faddeev model
Open this publication in new window or tab >>The supersymmetric extension of the Faddeev model
2004 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 381, no 1-2, p. 65-76Article in journal (Refereed) Published
Abstract [en]

We study the supersymmetric extension of the Faddeev model in four dimensions. The Faddeev model contains three-dimensional soliton solutions and we are interested in how these solitons are affected by supersymmetry. We consider both the N=1 and N=2 extensions and find that in neither case it is possible to supersymmetrize the model without adding additional bosonic terms. There are essentially two ways of constructing the supersymmetric theory, one that will lead to a model which allows for solitons and another that gives a model where solitons are excluded.

The N=2 model is studied since extending supersymmetry is the natural way of including topological charges in the algebra. A lower bound to the mass is obtained by computing the central charge. The result is that it is possible to have a nontrivial lower bound on the mass, this in principle allows for massive solitons.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-92025 (URN)10.1016/j.nuclphysb.2004.01.012 (DOI)
Available from: 2004-09-06 Created: 2004-09-06 Last updated: 2017-12-14Bibliographically approved
5. Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
Open this publication in new window or tab >>Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
2004 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 06, p. 010-Article in journal (Refereed) Published
Abstract [en]

We consider the scalar operators corresponding to semiclassical string states in AdS5 × S5 with the three angular momenta in S5 non-trivial. The string states recieve quantum corrections and we study the corresponding process on the gauge theory side. The anomalous dimension of the scalar operators is computed using the Bethe ansatz and we find the correction that corresponds to the energy of the quantized string. We restrict for simplicity to the case where two of the angular momenta in S5 are equal.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-92026 (URN)10.1088/1126-6708/2004/06/010 (DOI)
Available from: 2004-09-06 Created: 2004-09-06 Last updated: 2017-12-14Bibliographically approved

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