New Dualities of Supersymmetric Gauge Theories
New Dualities of Supersymmetric Gauge Theories

Author: Jörg Teschner

Publisher: Springer

Published: 2015-11-17

Total Pages: 467

ISBN-13: 3319187694

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This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

N=2 Supersymmetric Dynamics for Pedestrians
N=2 Supersymmetric Dynamics for Pedestrians

Author: Yuji Tachikawa

Publisher: Springer

Published: 2014-10-15

Total Pages: 236

ISBN-13: 331908822X

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Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

Supersymmetry
Supersymmetry

Author: Vladimir K. Dobrev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-09-24

Total Pages: 228

ISBN-13: 3110527499

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With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

Gauge/Gravity Duality
Gauge/Gravity Duality

Author: Martin Ammon

Publisher: Cambridge University Press

Published: 2015-04-09

Total Pages: 549

ISBN-13: 1107010349

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The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Gauge Field Theories
Gauge Field Theories

Author: Stefan Pokorski

Publisher: Cambridge University Press

Published: 2000-03-13

Total Pages: 636

ISBN-13: 9780521478168

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An expanded and up-dated book examining gauge theories and their symmetries.

Duality and Supersymmetric Theories
Duality and Supersymmetric Theories

Author: David I. Olive

Publisher: Cambridge University Press

Published: 1999-07-08

Total Pages: 496

ISBN-13: 9780521641586

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This is the first systematic introduction to electromagnetic duality and its generalisations. The authors are the leading figures in this exciting new area of mathematical physics, and their lectures have been organised not only to link with each other but also to describe the fundamental ideas, the latest developments, and some earlier work whose significance has only recently become apparent. This will be essential reading for all those working in mathematical physics.

Instanton Counting, Quantum Geometry and Algebra
Instanton Counting, Quantum Geometry and Algebra

Author: Taro Kimura

Publisher: Springer Nature

Published: 2021-07-05

Total Pages: 297

ISBN-13: 3030761908

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This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Dualities, Helicity Amplitudes, and Little Conformal Symmetry
Dualities, Helicity Amplitudes, and Little Conformal Symmetry

Author: Kitran Macey M. Colwell

Publisher: Springer

Published: 2017-11-11

Total Pages: 116

ISBN-13: 3319673920

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This book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly coupled. The calculations in this thesis suggest that this duality can also hold in the low-energy limit of nonsupersymmetric gauge theories. The idea of addressing the hierarchy problem of the standard model Higgs mechanism using conformal symmetry is also explored. Analogously to “Little Higgs” models, where divergences are cancelled only at one-loop order, models are studied that have infrared conformal fixed points which related gauge and Yukawa couplings, allowing for a cancellation between seemingly unrelated quantum loop diagrams.

Sixteenth International Congress on Mathematical Physics
Sixteenth International Congress on Mathematical Physics

Author: Pavel Exner

Publisher: World Scientific

Published: 2010

Total Pages: 709

ISBN-13: 981430462X

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The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.

String Theory And Cosmology - Proceedings Of The Nobel Symposium 127
String Theory And Cosmology - Proceedings Of The Nobel Symposium 127

Author: Ulf Danielsson

Publisher: World Scientific

Published: 2005-08-02

Total Pages: 107

ISBN-13: 9814479667

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The Nobel Symposium in 2003 on String Theory and Cosmology was a gathering of many of the most active and distinguished scientists in the world, including Stephen Hawking, 2004 Nobel Prize winner David Gross, and Andrei Linde. The experts, comprising both theoreticians and experimentalists, were given the opportunity to discuss the present status of their respective subjects. Throughout the symposium, special attention was given to the connections between the fields: the questions posed ranged from ”Can cosmology be used to test string theory?” to ”Can string theory answer deep questions about cosmology?” The symposium marked a new era in the understanding of the science of the very small and the very large. This book is a unique document that reflects upon the state of fundamental physics at a historically important moment in time.