Aspects of Supersymmetric Conformal Field Theories in Various Dimensions

Aspects of Supersymmetric Conformal Field Theories in Various Dimensions PDF Author: Emily Margaret Nardoni
Publisher:
ISBN:
Category :
Languages : en
Pages : 221

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Book Description
In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's $A,D,E$ singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional $N=1$ variants of supersymmetric QCD, with $U(N_c)$ or $SU(N_c)$ gauge group, $N_f$ fundamental flavors, and adjoint matter fields $X$ and $Y$ appearing in $W_{A,D,E}(X,Y)$ superpotentials. We explore these issues by considering various deformations of the $W_{A,D,E}$ superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional $N=1$ supersymmetric $SU(2)$ gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the $N=2$ Argyres-Douglas theory $H_0$, and a further deformation to an $N=1$ SCFT with low $a$ central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d $N=1$ quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus $g$ and $n$ punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees $p$ and $q$. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve $N=2$ supersymmetry, and derive terms that account for the local data at the punctures.

Aspects of Supersymmetric Conformal Field Theories in Various Dimensions

Aspects of Supersymmetric Conformal Field Theories in Various Dimensions PDF Author: Emily Margaret Nardoni
Publisher:
ISBN:
Category :
Languages : en
Pages : 221

Get Book Here

Book Description
In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's $A,D,E$ singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional $N=1$ variants of supersymmetric QCD, with $U(N_c)$ or $SU(N_c)$ gauge group, $N_f$ fundamental flavors, and adjoint matter fields $X$ and $Y$ appearing in $W_{A,D,E}(X,Y)$ superpotentials. We explore these issues by considering various deformations of the $W_{A,D,E}$ superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional $N=1$ supersymmetric $SU(2)$ gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the $N=2$ Argyres-Douglas theory $H_0$, and a further deformation to an $N=1$ SCFT with low $a$ central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d $N=1$ quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus $g$ and $n$ punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees $p$ and $q$. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve $N=2$ supersymmetry, and derive terms that account for the local data at the punctures.

New Dualities of Supersymmetric Gauge Theories

New Dualities of Supersymmetric Gauge Theories PDF 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.

An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry

An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry PDF Author: Ilarion V. Melnikov
Publisher: Springer
ISBN: 3030050858
Category : Science
Languages : en
Pages : 482

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Book Description
This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Quantum Non-linear Sigma-Models

Quantum Non-linear Sigma-Models PDF Author: Sergei V. Ketov
Publisher: Springer Science & Business Media
ISBN: 3662041928
Category : Science
Languages : en
Pages : 429

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Book Description
This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

Aspects of Supersymmetric Gauge Theories and Conformal Field Theories in Five and Three Dimensions

Aspects of Supersymmetric Gauge Theories and Conformal Field Theories in Five and Three Dimensions PDF Author: Julius Eckhard
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description


Points, Lines, and Surfaces at Criticality

Points, Lines, and Surfaces at Criticality PDF 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.

Nonperturbative Quantum Field Theory

Nonperturbative Quantum Field Theory PDF Author: G. Hooft
Publisher: Springer Science & Business Media
ISBN: 1461307295
Category : Science
Languages : en
Pages : 603

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Book Description
During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

Supersymmetric Gauge Field Theory and String Theory

Supersymmetric Gauge Field Theory and String Theory PDF Author: D. Bailin
Publisher: CRC Press
ISBN: 9781420050820
Category : Science
Languages : en
Pages : 672

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Book Description
Designed as a sequel to the authors' Introduction to Gauge Field Theory, Supersymmetric Gauge Field Theory and String Theory introduces first-year graduate students to supersymmetric theories, including supergravity and superstring theories. Starting with the necessary background in quantum field theory, the book covers the three key topics of high-energy physics. The emphasis is on practical calculations rather than abstract generalities or phenomenological results. Where possible, the authors show how to calculate, connecting the theoretical with the phenomenological. While the field continues to advance and grow, this book addresses the basic theory at the core and will likely remain relevant even if more advanced ideas change.

Introduction to Supersymmetric Field Theory

Introduction to Supersymmetric Field Theory PDF Author: Sergio M. Kuzenko
Publisher: CRC Press
ISBN: 9780750305068
Category : Science
Languages : en
Pages : 680

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Book Description
Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Superspace provides a comprehensive, detailed, and self-contained account of four dimensional simple supersymmetry and supergravity. Throughout the book, the authors cultivate their material in detail with calculations and full discussions of the fundamental ideas and motivations. They develop the subject in its superfield formulations but where appropriate for illustration, analogy, and comparison with conventional field theory, they use the component formulation. The book discusses many subjects that, until now, can only be found in the research literature. In addition, it presents a plethora of new results. Combining classical and quantum field theory with group theory, differential geometry, and algebra, the book begins with a solid mathematical background that is used in the rest of the book. The next chapter covers algebraic aspects of supersymmetry and the concepts of superspace and superfield. In the following chapters, the book presents classical and quantum superfield theory and the superfield formulation of supergravity. A synthesis of results and methods developed in the book, the final chapter concludes with the theory of effective action in curved superspaces. After studying this book, readers should be well prepared to pursue independent research in any area of supersymmetry and supergravity. It will be an indispensable source of reference for advanced graduate students, postdoctoral faculty, and researchers involved in quantum field theory, high energy physics, gravity theory, mathematical physics, and applied mathematics.

Conformal Field Theory

Conformal Field Theory PDF Author: Sergei V Ketov
Publisher: World Scientific
ISBN: 9814502529
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.