Quantum Superfield Supersymmetry

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Preface 6 Contents 7 1 Introduction 9 2 Effective Action and Loop Expansion: General Formulation 12 3 Superfield Description of Three-Dimensional Supersymmetric Theories 17 3.1 Definitions and Conventions 17 3.2 Field Theory Models 23 3.3 Non-Abelian Gauge Models 29 3.4 Quantum Description for the Superfield Models 31 3.5 Effective Action of the Three-Dimensional Superfield Theories and the Proper-Time Method 38 3.6 Supersymmetry in Three-Dimensional Space-Time and Noncommutativity 46 3.7 On the Noncommutativity in the Fermionic Sector of the Superspace 50 3.8 Conclusion 52 4 Four-Dimensional Superfield Supersymmetry 54 4.1 General Properties of the Four-Dimensional Superspace 54 4.2 Field Theory Models in the Four-Dimensional Superspace 62 4.2.1 Chiral Superfield Models 63 4.2.2 Abelian Gauge Superfield Model 65 4.2.3 Non-Abelian Gauge Theories 67 4.3 Generating Functional and Green Functions for Superfields 68 4.4 Feynman Supergraphs 74 4.5 Superficial Degree of Divergence. Renormalization 80 4.6 Effective Action in Superfield Theories. Superfield Proper-Time Technique 86 4.7 Problem of Superfield Effective Potential 90 4.8 The Wess-Zumino Model and a Problem of the Chiral Effective Potential 94 4.9 General Chiral Superfield Model 109 4.10 The Higher-Derivative Chiral Superfield Models 115 4.11 Supergauge Theories 126 4.11.1 General Description of Supergauge Theories 127 4.11.2 Background Field Method 134 4.11.3 Proper-Time Method for the Supergauge Theories 139 4.12 Conclusions 145 5 Supersymmetry Breaking 147 5.1 Explicit Supersymmetry Breaking 147 5.2 Spontaneous Supersymmetry Breaking 149 6 Conclusions 151 Bibliography 154 154 Index 159 This book presents the superfield description of various supersymmetric field theory models in three- and four-dimensional space-times. A mapping between superfield and component formulations of supersymmetric field theories is discussed. The author also describes the methodology for calculating quantum corrections in these theories employing supergraph formalism and functional methods, and illustrates these approaches with many detailed examples of how such calculations are performed for various superfield models.