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Published by Springer Nature Switzerland, 2023
ISBN 10: 3031281535 ISBN 13: 9783031281532
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book.This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules.The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2\* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction.The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory.This is an open access book.
Language: English
Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Taschenbuch. Condition: Neu. Branes and DAHA Representations | Sergei Gukov (u. a.) | Taschenbuch | vi | Englisch | 2023 | Springer | EAN 9783031281532 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by MP-AMM American Mathematical, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by Amer Mathematical Society, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, US, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Hardback. Condition: New. This volume contains lectures from the Graduate Summer School ""Quantum Field Theory and Manifold Invariants"" held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field.Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Language: English
Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
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ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
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Published by American Mathematical Society, IAS/Park City Mathematics Institute, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Published by American Mathematical Society, US, 2021
ISBN 10: 1470461234 ISBN 13: 9781470461232
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Hardback. Condition: New. This volume contains lectures from the Graduate Summer School ""Quantum Field Theory and Manifold Invariants"" held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field.Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
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Published by Springer Nature Switzerland Okt 2023, 2023
ISBN 10: 3031281535 ISBN 13: 9783031281532
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book.This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules.The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2\* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction.The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory.This is an open access book. 152 pp. Englisch.
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Published by Springer, Berlin|Springer Nature Switzerland|University of California, Berkeley Foundation|Springer, 2023
ISBN 10: 3031281535 ISBN 13: 9783031281532
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the chal.
Language: English
Published by Springer, Springer Aug 2023, 2023
ISBN 10: 3031281535 ISBN 13: 9783031281532
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Introduction.- 2d sigma-models and DAHA.- 3d theories and modularity.-4 d theories, fivebranes, and M-theory.- Appendix.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 152 pp. Englisch.