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BL
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| Record Number
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860108
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| Main Entry
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Münkler, Hagen
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| Title & Author
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Symmetries of Maldacena-Wilson loops from integrable string theory /\ Hagen Münkler.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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Springer theses
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| Page. NO
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1 online resource
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| ISBN
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3030036049
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: 3030036057
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: 9783030036041
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: 9783030036058
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9783030036041
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| Notes
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Doctoral Thesis accepted by the Humboldt-University Berlin, Berlin, Germany.
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Supervisor's Foreword; Abstract; Publications; Acknowledgements; Contents; 1 Introduction; References; 2 Symmetries, Fields and Loops; 2.1 Symmetries; 2.1.1 Conformal Symmetry; 2.1.2 =4 Superconformal Symmetry; 2.1.3 Yangian Symmetry; 2.2 =4 Supersymmetric Yang-Mills Theory; 2.3 The AdS/CFT Correspondence; 2.3.1 Anti-de Sitter Space; 2.3.2 The Correspondence; 2.4 The Maldacena-Wilson Loop; 2.4.1 Wilson Loops in Gauge Theories; 2.4.2 The Maldacena-Wilson Loop; 2.4.3 The Strong-Coupling Description; 2.4.4 The Circular Maldacena-Wilson Loop; 2.4.5 The Duality to Scattering Amplitudes
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4.3 Large Symmetry Transformations4.3.1 Analytical Deformations; 4.3.2 Numerical Deformations; 4.4 Infinitesimal Symmetry Transformations; 4.4.1 Variations of the Boundary Curves; 4.4.2 Evaluation of Conserved Charges; 4.5 Minimal Surfaces in S5; References; 5 Away from Strong Coupling; 5.1 Transferring Variations; 5.2 Transferring Generators; References; 6 Semisymmetric Space Models; 6.1 The String Action; 6.2 Integrability; 6.3 Master Symmetry; 6.4 Bonus Symmetries; References; 7 Minimal Surfaces in Superspace; 7.1 Poincaré Coordinates for the Supercoset; 7.2 The Superconformal Boundary
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7.3 The Bulk Expansion7.3.1 Equations of Motion; 7.3.2 Virasoro Constraints; 7.3.3 Variation of the Minimal Area; 7.4 Yangian Symmetry; 7.4.1 Level Zero; 7.4.2 Level One; References; 8 Conclusion and Outlook; References; Appendix; A.1 Spinor Conventions; A.1.1 Four-Dimensional Minkowski Space; A.1.2 Six-Dimensional Euclidean Space; A.1.3 Ten-Dimensional Minkowski Space; A.2 The Fundamental Representation of mathfraku(2,2 vert4); A.3 Matrix-Valued Differential Forms; A.4 Transformation of the Local Term; A.5 Densities of the Yangian Generators; A.5.1 Level Zero; A.5.2 Level 1; References
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| Abstract
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The book discusses hidden symmetries in the Anti-de Sitter/conformal field theory (AdS/CFT) duality. This duality is a modern concept that asserts an exact duality between conformally invariant quantum field theories and string theories in higher dimensional Anti-de Sitter spaces, and in this way provides a completely new tool for the study of strongly coupled quantum field theories. In this setting, the book focuses on the Wilson loop, an important observable in four-dimensional maximally supersymmetric gauge theory. The dual string description using minimal surfaces enables a systematic study of the hidden symmetries of the loop. The book presents major findings, including the discovery of a master symmetry for strings in general symmetric spaces, its relation to the Yangian symmetry algebra and its action on the minimal surfaces appearing in the dual string description of the Wilson loop. Moreover, it clarifies why certain symmetries are not present on the gauge theory side for purely bosonic Wilson loops and, lastly, how the supersymmetrization of the minimal surface problem for type IIB superstrings can be undertaken. As such, it substantially increases our understanding and use of infinite dimensional symmetries occurring in the AdS/CFT correspondence.
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| Subject
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Loops (Group theory)
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String models.
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Symmetry (Mathematics)
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Loops (Group theory)
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Mathematical modelling.
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MATHEMATICS-- Geometry-- General.
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Statistical physics.
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String models.
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Symmetry (Mathematics)
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| Dewey Classification
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516.1
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| LC Classification
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QA174.7.S96
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