Introduction To Conformal Field Theory

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Introduction to Conformal Field Theory

Ralph Blumenhagen,Erik Plauschinn
Introduction to Conformal Field Theory Book PDF

Author : Ralph Blumenhagen,Erik Plauschinn
Publisher : Springer
Page : 265 pages
File Size : 52,9 Mb
Release : 2009-07-11
Category : Science
ISBN : 9783642004506

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Introduction to Conformal Field Theory by Ralph Blumenhagen,Erik Plauschinn Pdf

Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.

A Mathematical Introduction to Conformal Field Theory

Martin Schottenloher
A Mathematical Introduction to Conformal Field Theory Book PDF

Author : Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 53,9 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540706908

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A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher Pdf

Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.

Conformal Field Theory

Philippe Francesco,Pierre Mathieu,David Senechal
Conformal Field Theory Book PDF

Author : Philippe Francesco,Pierre Mathieu,David Senechal
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461222569

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Conformal Field Theory by Philippe Francesco,Pierre Mathieu,David Senechal Pdf

Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Conformal Field Theory and Topology

Toshitake Kohno
Conformal Field Theory and Topology Book PDF

Author : Toshitake Kohno
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 55,6 Mb
Release : 2002
Category : Mathematics
ISBN : 082182130X

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Conformal Field Theory and Topology by Toshitake Kohno Pdf

Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.

EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions

Slava Rychkov
EPFL Lectures on Conformal Field Theory in D 3 Dimensions Book PDF

Author : Slava Rychkov
Publisher : Springer
Page : 72 pages
File Size : 49,7 Mb
Release : 2016-09-30
Category : Science
ISBN : 9783319436265

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EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions by Slava Rychkov Pdf

This primer develops Conformal Field Theory (CFT) from scratch, whereby CFT is viewed as any conformally-invariant theory that describes a fixed point of a renormalization group flow in quantum field theory. The book is divided into four lectures: Lecture 1 addresses the physical foundations of conformal invariance, while Lecture 2 examines the constraints imposed by conformal symmetry on the correlation functions of local operators, presented using the so-called projective null cone – a procedure also known as the embedding formalism. In turn, Lecture 3 focuses on the radial quantization and the operator product expansion, while Lecture 4 offers a very brief introduction to the conformal bootstrap. Derived from course-based notes, these lectures are intended as a first point of entry to this topic for Master and PhD students alike.

Introduction to Conformal Invariance and Its Applications to Critical Phenomena

Philippe Christe,Malte Henkel
Introduction to Conformal Invariance and Its Applications to Critical Phenomena Book PDF

Author : Philippe Christe,Malte Henkel
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 45,7 Mb
Release : 1993-04-13
Category : Science
ISBN : 9783540565048

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Introduction to Conformal Invariance and Its Applications to Critical Phenomena by Philippe Christe,Malte Henkel Pdf

The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.

Introduction to AdS/CFT Correspondence

Horaƫiu Năstase
Introduction to AdS CFT Correspondence Book PDF

Author : Horaƫiu Năstase
Publisher : Cambridge University Press
Page : 457 pages
File Size : 47,6 Mb
Release : 2015-09-10
Category : Science
ISBN : 9781107085855

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Introduction to AdS/CFT Correspondence by Horaƫiu Năstase Pdf

A pedagogical and self-contained introduction to AdS/CFT correspondence aimed at graduate students and researchers across theoretical physics.

Conformal Field Theory

Yavuz Nutku,Cihan Saclioglu,Teoman Turgut
Conformal Field Theory Book PDF

Author : Yavuz Nutku,Cihan Saclioglu,Teoman Turgut
Publisher : CRC Press
Page : 413 pages
File Size : 54,5 Mb
Release : 2018-03-14
Category : Science
ISBN : 9780429971426

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Conformal Field Theory by Yavuz Nutku,Cihan Saclioglu,Teoman Turgut Pdf

This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.

Introduction to Conformal Field Theory

Ralph Blumenhagen,Erik Plauschinn
Introduction to Conformal Field Theory Book PDF

Author : Ralph Blumenhagen,Erik Plauschinn
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 51,8 Mb
Release : 2009-07-31
Category : Science
ISBN : 9783642004490

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Introduction to Conformal Field Theory by Ralph Blumenhagen,Erik Plauschinn Pdf

Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.

Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes

Andreas Recknagel,Volker Schomerus
Boundary Conformal Field Theory and the Worldsheet Approach to D Branes Book PDF

Author : Andreas Recknagel,Volker Schomerus
Publisher : Cambridge University Press
Page : 349 pages
File Size : 53,9 Mb
Release : 2013-11-28
Category : Science
ISBN : 9781107511804

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Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by Andreas Recknagel,Volker Schomerus Pdf

Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and researchers in physics and mathematics.

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 : 41,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852880

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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.

String Field Theory

Harold Erbin
String Field Theory Book PDF

Author : Harold Erbin
Publisher : Springer Nature
Page : 424 pages
File Size : 43,9 Mb
Release : 2021-03-26
Category : Science
ISBN : 9783030653217

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String Field Theory by Harold Erbin Pdf

This textbook provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main focus of the book is the construction of the closed bosonic SFT. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, the reader is able to study the applications from the literature. The book is organized in two parts. The first part reviews the notions of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, the author outlines the proofs of several important properties such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed.

Conformal Field Theory

Sergei V Ketov
Conformal Field Theory Book PDF

Author : Sergei V Ketov
Publisher : World Scientific
Page : 502 pages
File Size : 41,8 Mb
Release : 1995-02-28
Category : Science
ISBN : 9789814502528

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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.

Basic Concepts of String Theory

Ralph Blumenhagen,Dieter Lüst,Stefan Theisen
Basic Concepts of String Theory Book PDF

Author : Ralph Blumenhagen,Dieter Lüst,Stefan Theisen
Publisher : Springer Science & Business Media
Page : 787 pages
File Size : 47,9 Mb
Release : 2012-10-03
Category : Science
ISBN : 9783642294976

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Basic Concepts of String Theory by Ralph Blumenhagen,Dieter Lüst,Stefan Theisen Pdf

The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.

Statistical Field Theory

G. Mussardo
Statistical Field Theory Book PDF

Author : G. Mussardo
Publisher : Oxford University Press
Page : 778 pages
File Size : 42,9 Mb
Release : 2010
Category : Science
ISBN : 9780199547586

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Statistical Field Theory by G. Mussardo Pdf

A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.