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Author: Yuji Tachikawa
Publisher: Springer
ISBN: 331908822X
Category : Science
Languages : en
Pages : 236
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Book Description
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.
Author: Yuji Tachikawa
Publisher: Springer
ISBN: 331908822X
Category : Science
Languages : en
Pages : 236
Get Book Here
Book Description
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.
Author: Sergio Cecotti
Publisher: Cambridge University Press
ISBN: 1107053811
Category : Mathematics
Languages : en
Pages : 425
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Book Description
Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.
Author: A. Ceresole
Publisher: Springer
ISBN:
Category : Medical
Languages : en
Pages : 552
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Book Description
The articles in this book are written versions of talks presented at a conference organized by the TMR network in Corfu. The main theme of the conference was the interconnection between string theory and gauge theory. These very recent developments draw from many aspects of string theory, supergravity and supersymmetric gauge field theory. For students starting their research there is a great deal of background material that they have to absorb in order to be able to follow current developments. With this in mind the editors have included pedagogical lectures on background material and recent developments. Extensive lecture notes by Bernard de Witt, Renate Kallosh, Robbert Dijkgraaf, Michael Green, Eliezer Rabinovici and John Schwarz make these proceedings a valuable reference for a long time to come. The book addresses researchers as well as students.
Author: Jörg Teschner
Publisher: Springer
ISBN: 3319187694
Category : Science
Languages : en
Pages : 467
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Book Description
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.
Author: Pavel Exner
Publisher: World Scientific
ISBN: 981430462X
Category : Science
Languages : en
Pages : 709
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Book Description
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.
Author: Pierre Deligne
Publisher: American Mathematical Society
ISBN: 0821820125
Category : Mathematics
Languages : en
Pages : 747
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Book Description
A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
Author: Edoardo Lauria
Publisher: Springer
ISBN: 3030257304
Category : Science
Languages : en
Pages : 173
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Book Description
This thesis offers a fascinating journey through various non-perturbative aspects of Conformal Theories, in particular focusing on the Conformal Bootstrap Programme and its extensions to theories with various degrees of symmetry. Because of the preeminent role of Conformal Theories in Nature, as well as the great generality of the results here obtained, this analysis directly applies to many different areas of research. The content of this thesis is certainly relevant for the physics community as a whole and this relevance is well motivated and discussed along the various chapters of this work. The work is self-contained and starts with an original introduction to conformal theories, defects in such theories and how they lead to constraints on data and an extension of the bootstrap programme. This situation is often realized by critical systems with impurities, topological insulators, or – in the high-energy context – by Wilson and 't Hooft operators. The thesis continues with original research results of the author, including supersymmetric extensions. These results may be relevant non only in the high energy physics context - where supersymmetry is required for the theory to be consistent - but also for condensed matter systems that enjoy supersymmetry emergence at long distances.
Author: Kentaro Hori
Publisher: American Mathematical Soc.
ISBN: 0821829556
Category : Mathematics
Languages : en
Pages : 954
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Book Description
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
Author: Ron Donagi, Michael R. Douglas
Publisher: American Mathematical Soc.
ISBN: 1470410516
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Author: Lars Brink
Publisher: World Scientific
ISBN: 9813144114
Category : Science
Languages : en
Pages : 403
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Book Description
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics.All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics.
