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Author: Marianne Heilmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
Author: Marianne Heilmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
Author: Timothy J Hollowood
Publisher: Springer Science & Business Media
ISBN: 3642363121
Category : Science
Languages : en
Pages : 78
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Book Description
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
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.
Author: Sevdiye Mutlu
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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Book Description
This thesis work is devoted to a detailed study of the renormalization group invariants (RG invariants) in minimal supersymmetric standard model (MSSM). The RG invariants are those Lagrangian parameters or combinations of the parameters, which exhibit no dependence on the energy scale up to the loop order with which the renormalization group equations (RGEs) are constructed. In this work, following an introductory chapter on standard model of electroweak and strong interactions as well as supersymmetry and supersymmetric field theories, we discuss construction of renormalization group equations in supersymmetric models, in particular, the minimal supersymmetric standard model with holomorphic and non-holomorphic soft terms. We finally concentrate on construction and phenomenological implications of the RG invariants in the minimal supersymmetric standard model with and without non-holomorphic supersymmetry breaking terms.
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.
Author: Diego Castano
Publisher:
ISBN: 9780530008080
Category : Science
Languages : en
Pages : 144
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Book Description
Abstract: This is the Ph. D. dissertation of the author and represents his research on the minimal supersymmetric extension of the standard model of particle physics. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Renormalization Group Study of the Minimal Supersymmetric Extension of the Standard Model With Softly Broken Supersymmetry" by Diego J. Castano, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.
Author: Daniel S. Freed
Publisher: American Mathematical Soc.
ISBN: 9780821871935
Category : Science
Languages : en
Pages : 132
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Book Description
The lectures featured in this book treat fundamental concepts necessary for understanding the physics behind these mathematical applications. Freed approaches the topic with the assumption that the basic notions of supersymmetric field theory are unfamiliar to most mathematicians. He presents the material intending to impart a firm grounding in the elementary ideas.
Author: Alexander Krasnitz
Publisher: World Scientific
ISBN: 9814543578
Category :
Languages : en
Pages : 238
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Book Description
The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
Author: Muller-kirsten Harald J W
Publisher: World Scientific Publishing Company
ISBN: 9813100966
Category : Science
Languages : en
Pages : 452
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Book Description
Supersymmetry is a symmetry which combines bosons and fermions in the same multiplet of a larger group which unites the transformations of this symmetry with that of spacetime. Thus every bosonic particle must have a fermionic partner and vice versa. Since this is not what is observed, this symmetry with inherent theoretical advantages must be badly broken. It is hoped that the envisaged collider experiments at CERN will permit a first experimental test, which is expected to revive the interest in supersymmetry considerably.This revised edition of the highly successful text of 20 years ago provides an introduction to supersymmetry, and thus begins with a substantial chapter on spacetime symmetries and spinors. Following this, graded algebras are introduced, and thereafter the supersymmetric extension of the spacetime Poincaré algebra and its representations. The Wess-Zumino model, superfields, supersymmetric Lagrangians, and supersymmetric gauge theories are treated in detail in subsequent chapters. Finally the breaking of supersymmetry is addressed meticulously. All calculations are presented in detail so that the reader can follow every step.
Author: A. Peter Young
Publisher: World Scientific
ISBN: 9810232403
Category : Science
Languages : en
Pages : 454
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Book Description
The last few years have seen many developments in the study of ?frustrated? systems, such as spin glasses and random fields. In addition, the application of the idea of spin glasses to other branches of physics, such as vortex lines in high temperature superconductors, protein folding, structural glasses, and the vulcanization of rubber, has been flourishing. The earlier reviews are several years old, so now is an appropriate time to summarize the recent developments. The articles in this book have been written by leading researchers and include theoretical and experimental studies, and large-scale numerical work (using state-of-the-art algorithms designed specifically for spin-glass-type problems), as well as analytical studies.
