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7. Basics and motivations 122
Chapter 8 Supersymmetric QCD and Seiberg duality Since four-dimensional supersymmetric Yang-Mills theories are expected to play a central role in the discovery of new physics in future experiments, it is essential to understand their main features. Their (eventual) application to the Nature strongly relies on our knowledge of how they may overcome the stringent bounds on new physics. As happens for many physical systems, included QCD, supersymmetric gauge theories present many phases, most of which are strongly coupled field theories. In this range of parameters where the perturbative expansion breaks down, we have to make use of other computational methods. In this section we analyze the physics of supersymmetric Yang-Mills theories and their lowenergy dynamics through the analysis of their effective Lagrangians. We concentrate on N = 1 supersymmetric field theories, as they do not suffer from the rigidity of extended supersymmetry while they still present the powerful of supersymmetric field theories, and can be embedded quite easy in string theory. We do not plan to be exhaustive. There are many textbooks [13, 99, 100] and reviews [101, 102, 103, 104, 105] on this subject. In Section 8.1 we give an overview on the general features of N = 1 supersymmetric field theories. In particular, we describe their phases, we explain how to write down a supersymmetric Lagrangian and find its low energy limit, and we show how to find its classical vacuum states. Section 8.2 is devoted to the case of Supersymmetric QCD (SQCD). We start by describing the low energy dynamics of pure Super Yang-Mills theory, then we apply the general arguments of Section 8.1 to the case of interacting matter fields, and argue that an electric/magnetic duality, namely Seiberg duality, exists. We discuss various aspects of this duality. We present a marginal deformation of SQCD in Section 8.3 and discuss how Seiberg duality is deformed in this case. 8.1 Generalities A gauge theory and its behavior are characterized by their symmetries and the way they are (or not) realized in the vacuum state. The original local symmetry of a gauge theory can be, for instance, completely spontaneously broken; otherwise, the vector bosons mediate long-range 123
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Università degli Studi di Milano-B
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Riassunto della tesi dimensionale.
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CONTENTS 4.3.2 The superpotential p
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List of Figures 3.1 New vertices pr
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Introduction and outline The advent
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Introduction and outline nonanticom
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Part I Nonanticommutative theories
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1. Basics and motivations ingredien
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1. Basics and motivations to obtain
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1. Basics and motivations 8
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2. Nonanticommutative superspace wh
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2. Nonanticommutative superspace wh
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2. Nonanticommutative superspace op
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3. The Wess-Zumino model We stress
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3. The Wess-Zumino model Φ 2 Φ U
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3. The Wess-Zumino model dim U(1)R
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3. The Wess-Zumino model • ω2 =
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4. Gauge theories ever, a modified
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4. Gauge theories They can be expre
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4. Gauge theories of the U(1) field
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4. Gauge theories and the pure gaug
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4. Gauge theories Since for the chi
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4. Gauge theories Figure 4.1: Gauge
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4. Gauge theories 4.2.2 Three-point
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4. Gauge theories 4.2.4 (Super)gaug
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4. Gauge theories and supergauge in
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4. Gauge theories where the trace o
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4. Gauge theories Figure 4.4: One-l
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4. Gauge theories fore, one-loop re
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4. Gauge theories α ˙α Γ dim R-
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4. Gauge theories 3. Gauge sector.
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4. Gauge theories We have introduce
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4. Gauge theories the covariant pro
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4. Gauge theories We note that the
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4. Gauge theories satisfy this set
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4. Gauge theories In order to cance
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4. Gauge theories of [22] the most
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4. Gauge theories By direct calcula
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4. Gauge theories pole coefficients
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4. Gauge theories superfields, in m
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4. Gauge theories 70 φ h ∂ Γ (a
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Page 95 and 96: Chapter 5 N = 2 Chern-Simons matter
Page 97 and 98: 5.2. Generalizations representation
Page 99 and 100: 5.2. Generalizations The superpoten
Page 101 and 102: Chapter 6 Quantization, fixed point
Page 103 and 104: 6.1. Quantization of N = 2 Chern-Si
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Page 107 and 108: 6.2. Two-loop renormalization and
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Page 111 and 112: In order to cancel the divergences
Page 113 and 114: 6.3. The spectrum of fixed points W
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Page 117 and 118: addition of flavor matter [83]. The
Page 119 and 120: 6.4. Infrared stability Figure 6.5:
Page 121 and 122: 6.4. Infrared stability Figure 6.6:
Page 123 and 124: 6.5. A relevant perturbation Figure
Page 125 and 126: 6.5. A relevant perturbation This k
Page 127: Part III Supersymmetry breaking 113
Page 130 and 131: 7. Basics and motivations where the
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Page 138 and 139: 8. Supersymmetric QCD and Seiberg d
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conclusions 172
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174
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A. Mathematical tools A.2 Useful in
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A. Mathematical tools For SU(N) we
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B. Feynman rules as f = ∇ 2 ∗ V
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B. Feynman rules Matter sector We n
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B. Feynman rules Since terms propor
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B. Feynman rules Φ ∇ α Φ ∇
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B. Feynman rules Here we recognize
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B. Feynman rules and contain an inf
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B. Feynman rules 192 ∂ φ Γ Γ
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C. Details on supersymmetry breakin
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BIBLIOGRAPHY [14] S. Penati and A.
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BIBLIOGRAPHY [47] M. Van Raamsdonk,
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BIBLIOGRAPHY [80] D. Gaiotto and A.
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BIBLIOGRAPHY [114] T. Banks and A.
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