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Magnon dispersion to four loops in the ABJM and ABJ models
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
2010 (English)In: Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, Vol. 43, no 27, p. 275402-Article in journal (Refereed) Published
Abstract [en]

The ABJM model is a superconformal Chern-Simons theory with N = 6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling-dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. The ABJM four-loop correction has mixed transcendentality, while the ABJ extension adds a term to the ABJM correction with highest transcendentality. We then compute the four-loop wrapping correction for a scalar operator in the 20 representation of SU (4) and find that it agrees with a recent prediction of the ABJM Y-system by Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.

Place, publisher, year, edition, pages
2010. Vol. 43, no 27, p. 275402-
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-136272DOI: 10.1088/1751-8113/43/27/275402ISI: 000278793100014OAI: oai:DiVA.org:uu-136272DiVA: diva2:376553
Available from: 2010-12-11 Created: 2010-12-11 Last updated: 2012-04-03Bibliographically approved
In thesis
1. Spins and Giants: Fundamental Excitations in Weakly and  Strongly Coupled ABJM Theory
Open this publication in new window or tab >>Spins and Giants: Fundamental Excitations in Weakly and  Strongly Coupled ABJM Theory
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The discovery of integrability on both sides of the duality between planar N=4 super Yang-Mills theory and free type IIB string theory in AdS5 × S5 has lead to great progress in our understanding of the AdS/CFT correspondence. Similar integrable structures also appear in the more recent three-dimensional superconformal N=6 Chern-Simons-matter theory constructed by Aharony, Bergman, Jafferis and Maldacena (ABJM), as well as in its gravity dual, type IIA string theory on AdS4 × CP3. However, new interesting complications arise in the AdS4/CFT3 duality. In the conjectured all-loop Bethe equations by Gromov and Vieira the dispersion relation of the magnons has a non-trivial coupling dependence which is parametrized by a function that is only known to the leading order at weak and strong coupling. In the first part of this thesis I discuss our calculations of the next-to-leading correction to this function at weak coupling. We compute this function from four-loop Feynman diagrams in the SU(2) × SU(2) sector of the ABJM model. As a consistency check we have performed the calculation both in a component formalism and using superspace techniques. At strong coupling the fundamental excitations of the integrable model are the giant magnons. The topic of the second part of this thesis is the spectrum of these giant magnons in CP3. Furthermore, I discuss our analyses of the finite-size corrections beyond the asymptotic Bethe ansatz. At weak coupling we have computed the leading four-loop wrapping diagrams in the ABJM model. At the strong coupling side of the duality I discuss our results for the exponentially suppressed finite-size corrections to the energy of giant magnons.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. p. 104
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 827
Keyword
String theory, AdS/CFT correspondence, Integrable field theory
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-151609 (URN)978-91-554-8082-0 (ISBN)
Public defence
2011-06-01, Å80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2011-05-11 Created: 2011-04-14 Last updated: 2011-07-01Bibliographically approved

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Minahan, Joseph A.

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