Modern Supersymmetry Dynamics and Duality

by Terning, John

• ISBN13: 9780198567639
• ISBN10: 0198567634
• Format: Hardcover
• Copyright: 2006-02-02
• Publisher: Oxford University Press

Summary

The book begins with a brief review of supersymmetry and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewing leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analyzing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersymmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "a-maximization". Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti-de-Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Supersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

Author Biography

John Terning Associate Professor of Physics Department of Physics University of California rne Shields Avenue Davis, CA 95616-8677 Associate Professor of Physics, University of California, Davis Japan Society for the Promotion of Science Fellowship: Apr. 96 Superconducting Super Collider Fellowship: Sept. 92 - Aug. 93 Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship: Sept. 90 - Aug. 92 Ph.D. in Physics, University of Toronto, advisor: Professor Bob Holdom, 1985-1990. M.Sc. in Physics, University of Toronto, advisor: Professor Bob Holdom, 1984-1985. B.Sc. in Physics, University of Alberta, 1980-1984.

Table of Contents

1 Introduction to supersymmetry	1	(18)
1.1 The unreasonable effectiveness of the Standard Model	1	(3)
1.2 SUSY algebra	4	(4)
1.3 SUSY representations	8	(3)
1.4 Extended SUSY	11	(4)
1.5 Central charges	15	(2)
References	17	(2)
2 SUSY Lagrangians	19	(24)
2.1 The free Wess–Zumino model	19	(2)
2.2 Commutators of SUSY transformations	21	(3)
2.3 The supercurrent and the SUSY algebra	24	(2)
2.4 The interacting Wess–Zumino model	26	(3)
2.5 SUSY Yang–Mills	29	(1)
2.6 SUSY gauge theories	30	(4)
2.7 Superspace	34	(4)
2.8 N = 0 SUSY	38	(3)
2.9 Exercises	41	(1)
References	41	(2)
3 SUSY gauge theories	43	(19)
3.1 Symmetries and group theory	43	(4)
3.2 Renormalization group	47	(5)
3.3 Quadratic divergence of the squark mass	52	(1)
3.4 Flat directions (classical moduli space)	53	(3)
3.5 The super Higgs mechanism	56	(4)
3.6 Exercises	60	(1)
References	61	(1)
4 The minimal supersymmetric standard model	62	(28)
4.1 Particles, sparticles, and their interactions	62	(5)
4.2 Electroweak symmetry breaking	67	(5)
4.3 The sparticle spectrum	72	(5)
4.4 Gauge coupling unification	77	(1)
4.5 Radiative electroweak symmetry breaking	78	(1)
4.6 One-loop correction to the Higgs mass	79	(2)
4.7 Precision electroweak measurements	81	(1)
4.8 Problems with flavor and CP	82	(4)
4.9 Exercises	86	(1)
References	86	(4)
5 SUSY breaking and the MSSM	90	(11)
5.1 Spontaneous SUSY breaking at tree-level	90	(3)
5.2 SUSY breaking scenarios	93	(2)
5.3 The goldstino	95	(2)
5.4 The goldstino theorem	97	(2)
5.5 Exercises	99	(1)
References	99	(2)
6 Gauge mediation	101	(7)
6.1 Messengers of SUSY breaking	101	(1)
6.2 RG calculation of soft masses	102	(3)
6.3 Gauge mediation and the μ problem	105	(1)
6.4 Exercise	106	(1)
References	106	(2)
7 Nonperturbative results	108	(25)
7.1 Monopoles	108	(5)
7.2 Anomalies in the path integral	113	(4)
7.3 Gauge anomalies	117	(1)
7.4 't Hooft's anomaly matching	118	(1)
7.5 Instantons	119	(2)
7.6 Instantons in broken gauge theories	121	(2)
7.7 NSVZ exact β function	123	(2)
7.8 Superconformal symmetry	125	(5)
References	130	(3)
8 Holomorphy	133	(12)
8.1 Non-renormalization theorems	133	(1)
8.2 Wavefunction renormalization	134	(1)
8.3 Integrating out	135	(1)
8.4 The holomorphic gauge coupling	136	(3)
8.5 Gaugino condensation	139	(2)
8.6 NSVZ revisited	141	(2)
8.7 Exercises	143	(1)
References	143	(2)
9 The Affleck-Dine-Seiberg superpotential	145	(12)
9.1 Symmetry and holomorphy	145	(3)
9.2 Consistency of WADS: moduli space	148	(2)
9.3 Consistency of WADS: mass perturbations	150	(2)
9.4 Generating WADS from instantons	152	(2)
9.5 Generating WADS from gaugino condensation	154	(1)
9.6 Vacuum structure	155	(1)
9.7 Exercise	155	(1)
References	155	(2)
10 Seiberg duality for SUSY QCD	157	(25)
10.1 Phases of gauge theories	157	(1)
10.2 The moduli space for F > or = to N	158	(2)
10.3 IR fixed points	160	(2)
10.4 Duality	162	(3)
10.5 Integrating out a flavor	165	(2)
10.6 Consistency	167	(1)
10.7 F = N: confinement with chiral symmetry breaking	168	(3)
10.8 F = N: consistency checks	171	(2)
10.9 F = N: + 1: s-confinement	173	(3)
10.10 Connection to theories with F > N + 1	176	(3)
10.11 Exercises	179	(1)
References	179	(3)
11 More Seiberg duality	182	(14)
11.1 The SO(N) moduli space	182	(2)
11.2 Duality for SO(N)	184	(2)
11.3 Some special cases	186	(1)
11.4 Duality for Sp(2N)	187	(2)
11.5 Why chiral gauge theories are interesting	189	(1)
11.6 S-Confinement	190	(2)
11.7 Deconfinement	192	(2)
11.8 Exercises	194	(1)
References	194	(2)
12 Dynamical SUSY breaking	196	(14)
12.1 A rule of thumb for SUSY breaking	196	(1)
12.2 The 3-2 model	196	(3)
12.3 The SU(5) model	199	(1)
12.4 SUSY breaking and deformed moduli spaces	200	(2)
12.5 SUSY breaking from baryon runaways	202	(3)
12.6 Direct gauge mediation	205	(2)
12.7 Single sector models	207	(1)
12.8 Exercise	208	(1)
References	208	(2)
13 The Seiberg-Witten theory	210	(23)
13.1 The Coulomb phase of N = 1 SO(N)	210	(4)
13.2 Diversion on SO(3)	214	(1)
13.3 The dyonic dual	215	(2)
13.4 Elliptic curves	217	(4)
13.5 N = 2: Seiberg-Witten	221	(4)
13.6 The Seiberg-Witten curve	225	(5)
13.7 Adding flavors	230	(1)
References	231	(2)
14 Superconformal field theories	233	(13)
14.1 A-Maximization	233	(1)
14.2 The simplest chiral SCFT	234	(5)
14.3 N = 2 and Argyres-Douglas points	239	(1)
14.4 N = 4 and orbifolds	240	(3)
References	243	(3)
15 Supergravity	246	(16)
15.1 Supergravity: on-shell	246	(1)
15.2 Supergravity: off-shell	247	(2)
15.3 Coupling to matter	249	(2)
15.4 10 and 11 dimensions	251	(7)
15.5 Five dimensions	258	(1)
15.6 Exercises	259	(1)
References	259	(3)
16 Anomaly and gaugino mediation	262	(13)
16.1 "Supergravity" mediation	262	(3)
16.2 SUSY breaking	265	(2)
16.3 The p problem	267	(2)
16.4 Slepton masses	269	(3)
16.5 Gaugino mediation	272	(1)
16.6 Exercise	273	(1)
References	273	(2)
17 Introduction to the AdS/CFT correspondence	275	(26)
17.1 D-brane constructions of gauge theories	275	(5)
17.2 The supergravity approximation	280	(5)
17.3 Spectra of CFT operators and AdS5 x S5 KK modes	285	(2)
17.4 Waves on AdS5	287	(2)
17.5 Nonperturbative static Coulomb potential	289	(1)
17.6 Breaking SUSY: finite temperature and confinement	290	(1)
17.7 The glueball mass gap	291	(3)
17.8 Breaking SUSY: orbifolds	294	(2)
17.9 Outlook	296	(1)
References	297	(4)
A Spinors and Pauli matrices	301	(4)
A.1 Conventions	301	(2)
A.2 Fierz and Pauli identities	303	(1)
A.3 Propagators	303	(2)
B Group theory	305	(4)
B.1 Classical Lie groups	305	(2)
B.2 SU(2)	307	(1)
B.3 SU(3)	307	(1)
B.4 SU(4)	308	(1)
References	309	(2)
Index	311