Conformal Field Theories And Tensor Categories

Conformal Field Theories And Tensor Categories Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Conformal Field Theories And Tensor Categories book. This book definitely worth reading, it is an incredibly well-written.

Conformal Field Theories and Tensor Categories

Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
Conformal Field Theories and Tensor Categories Book PDF

Author : Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 50,9 Mb
Release : 2013-10-30
Category : Mathematics
ISBN : 9783642393839

Get Book

Conformal Field Theories and Tensor Categories by Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert Pdf

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Lectures on Tensor Categories and Modular Functors

Bojko Bakalov,Alexander A. Kirillov
Lectures on Tensor Categories and Modular Functors Book PDF

Author : Bojko Bakalov,Alexander A. Kirillov
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 42,5 Mb
Release : 2001
Category : Abelian categories
ISBN : 9780821826867

Get Book

Lectures on Tensor Categories and Modular Functors by Bojko Bakalov,Alexander A. Kirillov Pdf

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

Tensor Categories and Endomorphisms of von Neumann Algebras

Marcel Bischoff,Yasuyuki Kawahigashi,Roberto Longo,Karl-Henning Rehren
Tensor Categories and Endomorphisms of von Neumann Algebras Book PDF

Author : Marcel Bischoff,Yasuyuki Kawahigashi,Roberto Longo,Karl-Henning Rehren
Publisher : Springer
Page : 94 pages
File Size : 52,7 Mb
Release : 2015-01-13
Category : Science
ISBN : 9783319143019

Get Book

Tensor Categories and Endomorphisms of von Neumann Algebras by Marcel Bischoff,Yasuyuki Kawahigashi,Roberto Longo,Karl-Henning Rehren Pdf

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

Quantum Groups, Quantum Categories and Quantum Field Theory

Jürg Fröhlich,Thomas Kerler
Quantum Groups Quantum Categories and Quantum Field Theory Book PDF

Author : Jürg Fröhlich,Thomas Kerler
Publisher : Springer
Page : 438 pages
File Size : 48,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540476115

Get Book

Quantum Groups, Quantum Categories and Quantum Field Theory by Jürg Fröhlich,Thomas Kerler Pdf

This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.

Tensor Categories

Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Tensor Categories Book PDF

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 55,5 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

Get Book

Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Lie Groups, Number Theory, and Vertex Algebras

Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Lie Groups Number Theory and Vertex Algebras Book PDF

Author : Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 53,6 Mb
Release : 2021-05-10
Category : Education
ISBN : 9781470453510

Get Book

Lie Groups, Number Theory, and Vertex Algebras by Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić Pdf

This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.

Dualizable Tensor Categories

Christopher L. Douglas,Christopher Schommer-Pries,Noah Snyder
Dualizable Tensor Categories Book PDF

Author : Christopher L. Douglas,Christopher Schommer-Pries,Noah Snyder
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 46,9 Mb
Release : 2021-06-18
Category : Education
ISBN : 9781470443610

Get Book

Dualizable Tensor Categories by Christopher L. Douglas,Christopher Schommer-Pries,Noah Snyder Pdf

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with cer-tain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-dimensional 3-framed local field theories. We also show that all finite tensor cat-egories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories. On the other hand, topological properties of 3-framed manifolds deter-mine algebraic equations among functors of tensor categories. We show that the 1-dimensional loop bordism, which exhibits a single full rotation, acts as the double dual autofunctor of a tensor category. We prove that the 2-dimensional belt-trick bordism, which unravels a double rotation, operates on any finite tensor category, and therefore supplies a trivialization of the quadruple dual. This approach pro-duces a quadruple-dual theorem for suitably dualizable objects in any symmetric monoidal 3-category. There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between piv-otal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.

Tensor Categories for Vertex Operator Superalgebra Extensions

Thomas Creutzig,Shashank Kanade,Robert McRae
Tensor Categories for Vertex Operator Superalgebra Extensions Book PDF

Author : Thomas Creutzig,Shashank Kanade,Robert McRae
Publisher : American Mathematical Society
Page : 194 pages
File Size : 44,8 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470467241

Get Book

Tensor Categories for Vertex Operator Superalgebra Extensions by Thomas Creutzig,Shashank Kanade,Robert McRae Pdf

View the abstract.

Vertex Operator Algebras and Related Areas

M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao
Vertex Operator Algebras and Related Areas Book PDF

Author : M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 53,5 Mb
Release : 2009-10-01
Category : Mathematics
ISBN : 9780821848401

Get Book

Vertex Operator Algebras and Related Areas by M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao Pdf

Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of two-dimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics. These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008. The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an up-to-date overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.

Lie Algebras, Vertex Operator Algebras, and Related Topics

Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Lie Algebras Vertex Operator Algebras and Related Topics Book PDF

Author : Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 42,5 Mb
Release : 2017-08-15
Category : Lie algebras
ISBN : 9781470426668

Get Book

Lie Algebras, Vertex Operator Algebras, and Related Topics by Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr Pdf

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Hopf Algebras, Tensor Categories and Related Topics

Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Hopf Algebras Tensor Categories and Related Topics Book PDF

Author : Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 46,6 Mb
Release : 2021-07-06
Category : Education
ISBN : 9781470456245

Get Book

Hopf Algebras, Tensor Categories and Related Topics by Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang Pdf

The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.

Vertex Algebras and Geometry

Thomas Creutzig,Andrew R. Linshaw
Vertex Algebras and Geometry Book PDF

Author : Thomas Creutzig,Andrew R. Linshaw
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 46,5 Mb
Release : 2018-07-20
Category : Geometry, Algebraic
ISBN : 9781470437176

Get Book

Vertex Algebras and Geometry by Thomas Creutzig,Andrew R. Linshaw Pdf

This book contains the proceedings of the AMS Special Session on Vertex Algebras and Geometry, held from October 8–9, 2016, and the mini-conference on Vertex Algebras, held from October 10–11, 2016, in Denver, Colorado. The papers cover vertex algebras in connection with geometry and tensor categories, with topics in vertex rings, chiral algebroids, the Higgs branch conjecture, and applicability and use of vertex tensor categories.

Conformal Field Theory

Sergei V Ketov
Conformal Field Theory Book PDF

Author : Sergei V Ketov
Publisher : World Scientific
Page : 502 pages
File Size : 49,7 Mb
Release : 1995-02-28
Category : Science
ISBN : 9789814502528

Get Book

Conformal Field Theory by Sergei V Ketov Pdf

Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and “conformal” intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.

Two-Dimensional Conformal Geometry and Vertex Operator Algebras

Yi-Zhi Huang
Two Dimensional Conformal Geometry and Vertex Operator Algebras Book PDF

Author : Yi-Zhi Huang
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242765

Get Book

Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang Pdf

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Renormalization and Effective Field Theory

Kevin Costello
Renormalization and Effective Field Theory Book PDF

Author : Kevin Costello
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 55,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852880

Get Book

Renormalization and Effective Field Theory by Kevin Costello Pdf

Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.