Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry
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perfield Approach to the Construction of Effective Action in Quantum Field Theory with Extended Supersymmetry I. L. Buchbindera, E. A. Ivanovb, and N. G. Pletneva, c, † a
Center for Theoretical Physics, Tomsk State Pedagogical University, Tomsk, 634061 Russia Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980 Russia cLaboratory of Theoretical Physics, Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia email: [email protected], [email protected] b
Abstract—We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the super field approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gaugeinvariant methods for constructing the lowenergy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of oneloop effective actions in ᏺ = 2 supersymmetric Yang–Mills theory with hypermultiplets and in ᏺ = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the lowenergy limit in superstring theory is discussed. DOI: 10.1134/S1063779616030035
CONTENTS 1. INTRODUCTION 2. ONELOOP EFFECTIVE ACTION IN ᏺ = 4 SUPERSYMMETRIC YANG–MILLS THEORY IN THE FORMALISM OF ᏺ = 1 SUPERSPACE 2.1. Introduction 2.2. ᏺ = 4 Supersymmetric Yang–Mills Theory 2.3. Superfield Formulations of ᏺ = 4 Supersymmetric Yang–Mills Theory 2.4. Formulation of ᏺ = 4 Supersymmetric Yang–Mills Theory in ᏺ = 1 Superspace 2.5. Formulation of ᏺ = 4 Supersymmetric Yang–Mills Theory in ᏺ = 2 Harmonic Superspace 2.6. Background Field Method in ᏺ = 1 Superspace 2.7. Calculation of Functional Traces and OneLoop Effective Action 2.8. Transformation of ᏺ = 1 Supersymmetric Effective Action into a Manifestly ᏺ = 2 Supersymmetric Form 2.9. Analysis of the Deformation of ᏺ = 4 Supersymmetry for the Effective Action in ᏺ = 2 Superspace †
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2.10. Summary 3. ONELOOP EFFECTIVE ACTION OF ᏺ = 4 SUPERSYMMETRIC YANG–MILLS THEORY IN HARMONIC SUPERSPACE 3.1. Introduction 3.2. ᏺ = 4 Supersymmetric Yang–Mills Theory in ᏺ = 2 Harmonic Superspace 3.3. OneLoop Effective Action in the Hypermultiplet Sector 3.4. Analysis of Superdiagrams for HypermultipletDependent Contributions to the Effective Action 3.5. Proper Time Representation for the Effective Action 3.6. Effective Action and Its Expansion in Covariant Spinor Derivatives 3.7. Useful Representation of the Baker–Campbell–Hausdorff Formula 3.8. Coefficient Functions in the Heat Kernel Expansion 3.9. Summary 4. HYPERMULTIPLET DEPENDENCE OF ONELOOP EFFECTIVE ACTION IN ᏺ = 2 SUPERCONFORMAL THEORIES 4.1. Introduction 4.2. Model and
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