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Author: Yan Gobeil
Publisher:
ISBN:
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Languages : en
Pages :
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Book Description
"In this thesis, we use three different sets of techniques to study the spectrum of Conformal Field Theories. We start by computing the conformal blocks for scalar thermal one-point functions in general dimensions. We achieve this by using three different methods: direct calculation, Casimir differential equation and Witten diagrams. These blocks are then used to find an asymptotic formula for the OPE coefficients of primary operators when two of them are heavy. The next part of the thesis uses the Lorentzian inversion formula to understand the low spin spectrum of specific CFTs. We look at the 3d Ising model and specifically describe how to obtain information about the $[\sigma\epsilon]_0$ Regge trajectory. We additionally use the same techniques to describe the low spin data of the critical $O(N)$ model at large $N$ in three dimensions. The third part of the thesis focusses on CFTs in two dimensions. We develop a new formulation for the conformal bootstrap by using the Virasoro fusion kernel. The identity kernel allows us to define Virasoro Mean Field Theory, which is the spectrum necessary in one channel to recover the identity in the other. We then use the new formulation of the crossing equation to show that this VMFT universally describes the large spin part of the CFT spectrum and we compute corrections to this universal behaviour"--
Author: Yan Gobeil
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"In this thesis, we use three different sets of techniques to study the spectrum of Conformal Field Theories. We start by computing the conformal blocks for scalar thermal one-point functions in general dimensions. We achieve this by using three different methods: direct calculation, Casimir differential equation and Witten diagrams. These blocks are then used to find an asymptotic formula for the OPE coefficients of primary operators when two of them are heavy. The next part of the thesis uses the Lorentzian inversion formula to understand the low spin spectrum of specific CFTs. We look at the 3d Ising model and specifically describe how to obtain information about the $[\sigma\epsilon]_0$ Regge trajectory. We additionally use the same techniques to describe the low spin data of the critical $O(N)$ model at large $N$ in three dimensions. The third part of the thesis focusses on CFTs in two dimensions. We develop a new formulation for the conformal bootstrap by using the Virasoro fusion kernel. The identity kernel allows us to define Virasoro Mean Field Theory, which is the spectrum necessary in one channel to recover the identity in the other. We then use the new formulation of the crossing equation to show that this VMFT universally describes the large spin part of the CFT spectrum and we compute corrections to this universal behaviour"--
Author: Edoardo Lauria
Publisher: Springer
ISBN: 3030257304
Category : Science
Languages : en
Pages : 164
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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: Ying-Hsuan Lin
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In this dissertation, we study bootstrap constraints on conformal field theories in two dimensions.
Author: Noriko Yui, Helena Verrill, and Charles F. Doran
Publisher: American Mathematical Soc.
ISBN: 9780821871577
Category : Duality (Mathematics)
Languages : en
Pages : 324
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Book Description
"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.
Author: David H. Meltzer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Slava Rychkov
Publisher: Springer
ISBN: 3319436260
Category : Science
Languages : en
Pages : 81
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Book Description
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.
Author: Marc Gillioz
Publisher: Springer Nature
ISBN: 303127086X
Category : Science
Languages : en
Pages : 93
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Book Description
This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject. This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.
Author: Wen-Jie Ma
Publisher:
ISBN:
Category :
Languages : en
Pages : 162
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Book Description
Conformal field theories (CFTs) play a central role in modern theoretical physics. The study of CFTs leads to a deep understanding of both string theory and condensed matter physics. In a CFT, correlation functions are essential ingredients for the computation of physical observables. Due to the existence of the operator product expansion (OPE), conformal correlation functions can be separated into their dynamical parts, which constitute of the OPE coefficients as well as the conformal dimensions, and their kinematic parts, dubbed the conformal blocks, which are completely fixed by conformal symmetry. Since the conformal bootstrap was revived in 2008, several techniques have been developed to compute the four-point conformal blocks during the last decade. In contrast to the four-point blocks, conformal blocks with more than four points, which are notoriously difficult to compute, have not been studied in great detail, although these higher-point conformal blocks are useful for the implementation of higher-point conformal bootstrap as well as the study of AdS Witten diagrams. In this thesis, by using the embedding space OPE, we obtain expressions for the scalar M-point conformal blocks with scalar exchanges in the comb configuration as well as scalar six-and seven-point conformal blocks with scalar exchanges in the snowflake and extended snowflake configurations. Moreover, we propose a set of Feynman-like rules to directly write down an explicit form for any global conformal block in one and two dimensions. Based on the position space OPE, we prove the Feynman-like rules by construction. Finally, after discussing the symmetry properties of the conformal blocks, we develop a systematical way to write down the bootstrap equations for higher-point correlation functions.
Author: Luca Victor Iliesiu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Serge? Vladimirovich Ketov
Publisher: World Scientific
ISBN: 9810216084
Category : Science
Languages : en
Pages : 502
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Book Description
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.
