N 2 Supersymmetric Dynamics For Pedestrians

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N 2 Supersymmetric Dynamics For Pedestrians

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Author : Yuji Tachikawa
language : en
Publisher: Springer
Release Date : 2014-10-15

N 2 Supersymmetric Dynamics For Pedestrians written by Yuji Tachikawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-15 with Science categories.

Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

Supersymmetry From The Basics To Exact Results In Gauge Theories

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Author : Matteo Bertolini
language : en
Publisher: World Scientific
Release Date : 2024-10-29

Supersymmetry From The Basics To Exact Results In Gauge Theories written by Matteo Bertolini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-29 with Science categories.

What is Supersymmetry? Is it something real? If not, can it be useful in any way? This book, structured as a textbook for a one semester graduate course on supersymmetry, provides an introduction to this fascinating subject and seeks to answer these questions.Theoretically inclined in its contents, the book can be divided into three parts. The first part introduces the supersymmetry algebra and its representations, and provides a detailed description of the superfield formalism. The second part focuses on the construction of supersymmetric field theories; it includes an overview on non-renormalization theorems, the analysis of several examples of tree-level supersymmetry breaking and a discussion of the basic structure of supersymmetric models for describing physics beyond the Standard Model. The third part discusses the quantum behavior of supersymmetric (gauge) theories, in which holomorphy and dualities play a prominent role. The reader will become familiar with topics like Seiberg duality, dynamical supersymmetry breaking (both in stable and metastable vacua), Seiberg-Witten theory, Argyres-Douglas fixed points, S-duality and more. Several exercises at the end of each chapter will allow readers to test their understanding, discuss some extensions, or prove statements from the main text.

An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry

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Author : Ilarion V. Melnikov
language : en
Publisher: Springer
Release Date : 2019-02-11

An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry written by Ilarion V. Melnikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-11 with Science categories.

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.

New Dualities Of Supersymmetric Gauge Theories

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Author : Jörg Teschner
language : en
Publisher: Springer
Release Date : 2015-11-17

New Dualities Of Supersymmetric Gauge Theories written by Jörg Teschner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-17 with Science categories.

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.

Space Time Matter

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Author : Jochen Brüning
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-09

Space Time Matter written by Jochen Brüning and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Instanton Counting Quantum Geometry And Algebra

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Author : Taro Kimura
language : en
Publisher: Springer Nature
Release Date : 2021-07-05

Instanton Counting Quantum Geometry And Algebra written by Taro Kimura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Science categories.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Six Dimensional Superconformal Field Theories And Their Torus Compactifications

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Author : Kantaro Ohmori
language : en
Publisher: Springer
Release Date : 2018-11-03

Six Dimensional Superconformal Field Theories And Their Torus Compactifications written by Kantaro Ohmori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Science categories.

This thesis describes the structures of six-dimensional (6d) superconformal field theories and its torus compactifications. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to four-dimensional superconformal field theories in the class, called class S. It is known that compactifications of 6d conformal field theories with maximal supersymmetries provide numerous insights into four-dimensional superconformal field theories. This thesis generalizes the story to the theories with smaller supersymmetry, constructing those six-dimensional theories as brane configurations in the M-theory, and highlighting the importance of fractionalization of M5-branes. This result establishes new dualities between the theories with eight supercharges.

The Indian National Bibliography

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Author :
language : en
Publisher:
Release Date : 2017-04

The Indian National Bibliography written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04 with India categories.

High Energy Physics Index

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Author :
language : en
Publisher:
Release Date : 1987

High Energy Physics Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Nuclear physics categories.

Modern Quantum Field Theory

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Author : Tom Banks
language : en
Publisher: Cambridge University Press
Release Date : 2008-09-18

Modern Quantum Field Theory written by Tom Banks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-18 with Science categories.

Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.