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Spins and Giants: Fundamental Excitations in Weakly and  Strongly Coupled ABJM Theory
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
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. , 104 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 827
Keyword [en]
String theory, AdS/CFT correspondence, Integrable field theory
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-151609ISBN: 978-91-554-8082-0OAI: oai:DiVA.org:uu-151609DiVA: diva2:410760
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
List of papers
1. Magnon dispersion to four loops in the ABJM and ABJ models
Open this publication in new window or tab >>Magnon dispersion to four loops in the ABJM and ABJ models
2010 (English)In: Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, Vol. 43, no 27, 275402- p.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.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-136272 (URN)10.1088/1751-8113/43/27/275402 (DOI)000278793100014 ()
Available from: 2010-12-11 Created: 2010-12-11 Last updated: 2012-04-03Bibliographically approved
2. Superspace calculation of the four-loop spectrum in N = 6 supersymmetric Chern-Simons theories
Open this publication in new window or tab >>Superspace calculation of the four-loop spectrum in N = 6 supersymmetric Chern-Simons theories
Show others...
2010 (English)In: Journal of High Energy Physics (JHEP), ISSN 1029-8479, E-ISSN 1126-6708, no 12, 074- p.Article in journal (Refereed) Published
Abstract [en]

Using N = 2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h(2)(lambda) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h(2)(lambda) that interpolates between weak and strong couplings.

Keyword
Supersymmetric gauge theory, Superspaces, AdS-CFT Correspondence, Integrable Field Theories
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-142588 (URN)10.1007/JHEP12(2010)074 (DOI)000285964200018 ()
Available from: 2011-01-14 Created: 2011-01-14 Last updated: 2012-04-05Bibliographically approved
3. A limit on the ABJ model
Open this publication in new window or tab >>A limit on the ABJ model
2010 (English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-142593 (URN)
Note
To appear in the proceedings of 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 2009Available from: 2011-01-14 Created: 2011-01-14 Last updated: 2012-04-03
4. Finite size giant magnons in the SU(2) × SU(2) sector of AdS4 × CP3
Open this publication in new window or tab >>Finite size giant magnons in the SU(2) × SU(2) sector of AdS4 × CP3
2008 (English)In: Journal of High Energy Physics (JHEP), ISSN 1029-8479, Vol. 12, 073- p.Article in journal (Refereed) Published
Abstract [en]

We use the algebraic curve and Lüscher's μ-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) × SU(2) sector of AdS4 × CP3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) × SU(2) sector.

Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-87409 (URN)10.1088/1126-6708/2008/12/073 (DOI)
Available from: 2008-12-17 Created: 2008-12-17 Last updated: 2011-07-01Bibliographically approved
5. Dyonic Giant Magnons in CP3: Strings and Curves at Finite J
Open this publication in new window or tab >>Dyonic Giant Magnons in CP3: Strings and Curves at Finite J
2009 (English)In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 80, no 2, 026005- p.Article in journal (Refereed) Published
Abstract [en]

This paper studies giant magnons in AdS4×CP3 using both the string sigma model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalization of the CP1string solution, which matches the “small” giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the “big” giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the nondyonic cases always match the Arutyunov-Frolov-Zamaklar result. For the dyonic RP3 magnon we recover the S5answer, but for the small and big giant magnons we obtain new corrections.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-107660 (URN)10.1103/PhysRevD.80.026005 (DOI)000268618800126 ()
Projects
Gauge/string duality
Available from: 2009-08-22 Created: 2009-08-22 Last updated: 2011-07-01Bibliographically approved

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