Supersymmetry: From the Basics to Exact Results in Gauge Theories

Contents
Preface
Foreword
1. Supersymmetry: A Bird’s Eye View
	1.1 What is supersymmetry?
	1.2 Why supersymmetry?
		1.2.1 Theoretical reasons
		1.2.2 Phenomenological reasons
		1.2.3 Supersymmetry as a theoretical lab for strongly coupled gauge dynamics
	1.3 Some useful textbooks
2. The Supersymmetry Algebra
	2.1 Lorentz and Poincar´e groups
	2.2 Spinors and representations of the Lorentz group
	2.3 The supersymmetry algebra
	2.4 Exercises
	References
3. Representations of the Supersymmetry Algebra
	3.1 Massless supermultiplets
	3.2 Massive supermultiplets
	3.3 Representation on fields: a first try
	3.4 Exercises
	References
4. Superspace and Superfields
	4.1 Superspace as a coset
	4.2 Superfields as fields in superspace
	4.3 Supersymmetric invariant actions — general philosophy
	4.4 Chiral superfields
	4.5 Real (aka Vector) superfields
	4.6 (Super)Current superfields
		4.6.1 Internal symmetry current superfields
		4.6.2 Supercurrent superfields
	4.7 Exercises
	References
5. Supersymmetric Actions: Minimal Supersymmetry
	5.1 N = 1 matter actions
		5.1.1 Non-linear sigma model I
	5.2 N = 1 supersymmetric Yang-Mills
	5.3 N = 1 gauge-matter actions
		5.3.1 Classical moduli space: Examples
		5.3.2 Non-linear sigma model II
	5.4 Exercises
	References
6. Supersymmetric Actions: Extended Supersymmetry
	6.1 N = 2 supersymmetric actions
		6.1.1 Non-linear sigma model III
	6.2 N = 4 supersymmetric actions
	6.3 On non-renormalization theorems
	6.4 Exercises
	References
7. Spontaneous Supersymmetry Breaking
	7.1 Vacua in supersymmetric theories
	7.2 Goldstone theorem and the goldstino
	7.3 F-term breaking
	7.4 Pseudo-moduli space: quantum corrections
	7.5 D-term breaking
	7.6 Indirect criteria for supersymmetry breaking
		7.6.1 Supersymmetry breaking and global symmetries
		7.6.2 Topological constraints: the Witten Index
		7.6.3 Genericity and metastability
	7.7 Exercises
	References
8. Supersymmetric Extensions of the Standard Model
	8.1 Towards dynamical supersymmetry breaking
	8.2 The supertrace mass formula
	8.3 Beyond the MSSM
	8.4 Spurions, soft terms and the messenger paradigm
	8.5 Mediating the breaking
		8.5.1 Gravity mediation
		8.5.2 Gauge mediation
	8.6 Exercises
	References
9. Non-perturbative Effects and Holomorphy
	9.1 Instantons in a nutshell
	9.2 Anomalies in a nutshell
	9.3 ’t Hooft anomaly matching condition
	9.4 Holomorphy
	9.5 Holomorphy and non-renormalization theorems
	9.6 Holomorphic decoupling
	9.7 Exercises
	References
10. Supersymmetric Gauge Dynamics: Minimal Supersymmetry
	10.1 Confinement and mass gap in QCD, YM and SYM
		10.1.1 Intermezzo: Wilson loops as order parameters for confinement
	10.2 Phases of gauge theories: examples
		10.2.1 Coulomb phase and free phase
		10.2.2 Continuously connected phases
	10.3 N=1 SQCD: perturbative analysis
	10.4 N=1 SQCD: non-perturbative dynamics
		10.4.1 Pure SYM: gaugino condensation
		10.4.2 F < N: the ADS superpotential
		10.4.3 Integrating in and out: the linearity principle
		10.4.4 F ≥ N: persistent moduli space
		10.4.5 Conformal window
		10.4.6 N = 1 electric-magnetic duality
	10.5 The phase diagram of N=1 SQCD
	References
11. Dynamical Supersymmetry Breaking
	11.1 Calculable and non-calculable models: generalities
	11.2 The one GUT family SU(5) model
	11.3 The 3-2 model: supersymmetry breaking by instantons
	11.4 The 4-1 model: supersymmetry breaking by gaugino condensation
	11.5 ITIY model: supersymmetry breaking with classical flat directions
	11.6 DSB into metastable vacua. A case study: massive SQCD
		11.6.1 Massive SQCD in the free magnetic phase: electric description
		11.6.2 Massive SQCD in the free magnetic phase: magnetic description
		11.6.3 Summary of the physical picture
	11.7 Exercises
	References
12. Supersymmetric Gauge Dynamics: Extended Supersymmetry
	12.1 Low energy effective actions: classical and quantum
		12.1.1 N = 2 effective actions
		12.1.2 N = 4 effective actions
	12.2 Monopoles, dyons and electro-magnetic duality
		12.2.1 The Georgi-Glashow model and its (supersymmetric) generalizations
	12.3 Seiberg-Witten theory
		12.3.1 N = 2 SU(2) pure SYM
		12.3.2 Intermezzo: confinement by monopole condensation
	12.4 Seiberg-Witten theory: generalizations
		12.4.1 A case study: N = 2 SU(2) SQCD with one flavor
	12.5 N = 4: Montonen-Olive duality
	12.6 Exercises
	References
Index