School and conference on modular forms and mock modular. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. This survival kit attempts to provide the reader with the most i mportant techniques and results of this fascinating topic for immediate use in the string theory lectures. Conformal prediction for reliable machine learning theory, adaptations and applications morgan kaufmann vineeth balasubramanian, shenshyang ho, vladimir vovk. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. Philippe di francesco pierre mathieu david senechal springer, new york, 1997 isbn 038794785x. Conformal field theory philippe francesco springer.
Introduction to conformal field theory antonin rovai introduction these lecture notes consist of an elementary introduction to conformal field theory cft. A conformal eld theory is a quantum eld theory which has cas a classical symmetry of the action. Its origins can be traced back on the one hand to statistical mechanics, and on the. But you soon realise that its big because it starts at. The aim of these notes is to give a pedagogical introduction to the subject in two and higher dimensions, where standard textbook material will be supplemented by more modern techniques. An elementary introduction to conformal field theory is given. Chapters 5 and 6 dealt with general properties of twodimensional conformal field theories. Pdf conformal data from finite entanglement scaling. Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles.
In two dimensions, there is an infinitedimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. The links below provide errata on the first and second printing on the book. Over the last several decades, our understanding of conformal eld theories has advanced signi cantly. Schottenloher, a mathematical introduction to conformal field theory. Its scop e is limited to certain simple asp ects of the theory of conformally in v arian t quan tum elds in t w o spacetime dimensions. Bits and pieces in logarithmic conformal field theory michael flohr institute for theoretical physics, university of hannover. Related content logarithmic conformal field theory. These lectures notes are based on 8 3 hours of lectures given for graduate students. Topics include free bosons and fermions, orbifolds, affine lie algebras, coset conformal field theories.
The present chapter is devoted to particularly simple conformal theories called minimal models. Conformal field theory, di francesco, p mathieu 1997 conformal field theory, sv ketov 1995 nonperturbative field theory. The first comprehensive physics textbook on cft was maybe. The assumption that the scaling hypothesis holds for this kind of. Consequently, conformal eld theory is a very broad subject. The treatment is selfcontained, pedagogical, and exhaustive, and includes a. For any higher dimension, conformal invariance is nothing more than the invariance under translations, dilations, rotations and special conformal transformations, but, in two dimensions, the conformal virasoroalgebra turns out to be in. The litmus test for guring out when a quantum eld theory in a xed background space. An introduction to conformal field theory to cite this article.
There are some nice discussions at the beginning regarding conformal symmetries in general dimensions. Axiomatic conformal field theory now, guided by the axioms of quantum field theory we attempt at constructing a number of axioms for quantum conformal field theory or cft for short. On the theory side, many exact results in 1d can be obtained by a blend of methods that comprises lattice integrability 12, and nonperturbative. It should be clear that adding a mass term r d 2xm 2 to the theory breaks con formal invariance. However, i dont really see how to exponentiate the infinitesimal form to actually get to the finite form.
Henkel, conformal invariance and critical phenomena, springer 1999 k. They are intended as an introduction to conformal field theories in various dimensions. Bits and pieces in logarithmic conformal field theory. I thank numerous participants at the conformal eld theory workshop at the aspen center for physics aug. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. In some cases, this allows them to be solved exactly, using the conformal bootstrap method. Conformal field theory applied to loop models springerlink. Conformal field theory luis fernando alday conformal eld theory is a vast subject. A twodimensional conformal field theory is a quantum field theory on a euclidean twodimensional space, that is invariant under local conformal transformations in contrast to other types of conformal field theories, twodimensional conformal field theories have infinitedimensional symmetry algebras. Part i deals with conformal eld theory, in particular twodimensional conformal eld theory, while part ii is concerned with. The treatment is selfcontained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, lie algebras and. Question about derivation of tensor in di francescos cft. Pdf lectures on conformal field theory semantic scholar. In 2d, the infinitedimensional algebra of local conformal transformations normally permits exact solution or classification of such theories.
Statistical physics, complex systems and conformal field. Almost all the quantum eld theories we study, when coupled to gravity, will be di eomorphism invariant. Newest conformalfieldtheory questions physics stack. Conformal field theory graduate texts in contemporary. These theories are characterized by a hilbert space made of a finite number of representations of the virasoro algebra verma modules.
The application to string theory was explained by friedan, martinec and shenker in conformal invariance, supersymmetry and string theory, nucl. Rehren, konforme quantenfeldtheorie in german, lecture notes, a pdf file is available on rehrens homepage m. The standard topics in perturbative string theory are covered, including some basic conformal field theory, tduality and d branes. These lectures notes are based on courses given at national taiwan university, national chiaotung university, and national tsing hua university in the spring term of 2015. The relevance to equilibrium statistical mechanics makes. It indicates that the product of two conformal elds evaluated at di erent points can be expanded as another local eld times a numerical coe cient depending on the di erence between the points in question or written schematically. These lecture notes cover a number of introductory topics in the area of string theory, and are intended as a foundation for many of the other lecture courses in tasi 2003. Matthias gaberdiel the topics are organized in two main parts. Conformal field theory of the flory model of protein melting, phys. For d 2 the explicit dependence cancels out, and this demonstrates part of the conformal symmetry of the action. As we had anticipated the key concept is that of a. This is a question for anyone who is familiar with di francesco s book on conformal field theory.
A conformal field theory is a quantum field theory that is invariant under conformal transformations. While this approach is widely recognized as very powerful, much of the literature uses it alongside the lagrangian approach. Segal, the definition of conformal field theory, preprint 1988. Snchal errata on second printing these errata and eventual additional ones are listed on the following web page. Conformal field theory for inhomogeneous onedimensional. This class of theories have the property that they are invariant under so called conformal transformations, that. Introduction conformal field theory has been an important tool in theoretical physics during the last decade.
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