Perturbative and non-perturbative infrared behavior of ...
Perturbative and non-perturbative infrared behavior of ...
Perturbative and non-perturbative infrared behavior of ...
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CONTENTS<br />
4.3.2 The superpotential problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 45<br />
4.3.3 The solution to the superpotential problem . . . . . . . . . . . . . . . . . . 46<br />
4.3.4 The most general gauge invariant action . . . . . . . . . . . . . . . . . . . . 47<br />
4.3.5 One–loop renormalizability <strong>and</strong> gauge invariance . . . . . . . . . . . . . . . 52<br />
4.4 An explicit case: the U(1) theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
4.4.1 U∗(1) NAC SYM theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
4.4.2 One flavor case: Renormalization <strong>and</strong> β–functions . . . . . . . . . . . . . . 63<br />
4.4.3 Three–flavor case: Renormalization <strong>and</strong> β-functions . . . . . . . . . . . . . 66<br />
4.4.4 Finiteness, fixed points <strong>and</strong> IR stability . . . . . . . . . . . . . . . . . . . . 69<br />
4.5 Summary <strong>and</strong> conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75<br />
II Three-dimensional field theories 79<br />
5 N = 2 Chern-Simons matter theories 81<br />
5.1 The ABJM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82<br />
5.2 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83<br />
6 Quantization, fixed points <strong>and</strong> RG flows 87<br />
6.1 Quantization <strong>of</strong> N = 2 Chern–Simons matter theories . . . . . . . . . . . . . . . . 88<br />
6.2 Two–loop renormalization <strong>and</strong> β–functions . . . . . . . . . . . . . . . . . . . . . . 93<br />
6.2.1 One loop results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93<br />
6.2.2 Two-loop results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
6.3 The spectrum <strong>of</strong> fixed points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98<br />
6.3.1 Theories without flavors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98<br />
6.3.2 Theories with flavors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
6.4 Infrared stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104<br />
6.4.1 Theories without flavors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105<br />
6.4.2 Theories with flavors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107<br />
6.5 A relevant perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109<br />
III Supersymmetry breaking 113<br />
7 Basics <strong>and</strong> motivations 115<br />
7.1 The supertrace theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115<br />
7.2 Non-renormalizable interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
7.3 Mediating the supersymmetry breaking effects: an overview . . . . . . . . . . . . . 119<br />
7.4 R-parity <strong>and</strong> R-symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120<br />
8 Supersymmetric QCD <strong>and</strong> Seiberg duality 123<br />
8.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123<br />
8.1.1 Supersymmetric Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . 125<br />
8.1.2 The vacuum state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126<br />
8.2 Supersymmetric QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127<br />
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