Supersymmetry and String Theory
Beyond the Standard Model
By Michael Dine
Publisher: Cambridge University Press
Print Publication Year: 2007
Online Publication Date:May 2010
Online ISBN:9780511618482
Hardback ISBN:9780521858410
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511618482.012
Subjects: Particle Physics and Nuclear Physics, Theoretical Physics and Mathematical Physics
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In a standard advanced field theory course, one learns about a number of symmetries: Poincaré invariance, global continuous symmetries, discrete symmetries, gauge symmetries, approximate and exact symmetries. These latter symmetries all have the property that they commute with Lorentz transformations, and in particular they commute with rotations. So the multiplets of the symmetries always contain particles of the same spin; in particular, they always consist of either bosons or fermions.
For a long time, it was believed that these were the only allowed types of symmetry; this statement was even embodied in a theorem, known as the Coleman– Mandula theorem. However, physicists studying theories based on strings stumbled on a symmetry which related fields of different spin. Others quickly worked out simple field theories with this new symmetry: supersymmetry.
Supersymmetric field theories can be formulated in dimensions up to eleven. These higher-dimensional theories will be important when we consider string theory. In this chapter, we consider theories in four dimensions. The supersymmetry charges, because they change spin, must themselves carry spin – they are spin-1/2 operators. They transform as doublets under the Lorentz group, just like the two component spinors X and X*. (The theory of two-component spinors is reviewed in Appendix A, where our notation, which is essentially that of the text by Wess and Bagger (1992), is explained). There can be 1, 2, 4 or 8 such spinors; correspondingly, the symmetry is said to be N = 1, 2, 4 or 8 supersymmetry. Like generators of an ordinary group, the supersymmetry generators obey an algebra; unlike an ordinary bosonic group, however, the algebra involves anticommutators as well as commutators (it is said to be “graded”).
pp. i-vi
pp. vii-xiv
pp. xv-xvii
A note on choice of metric: Read PDF
pp. xviii-xix
pp. xx-xx
Part 1 - Effective field theory: the Standard Model, supersymmetry, unification: Read PDF
pp. 1-2
1 - Before the Standard Model: Read PDF
pp. 3-8
2 - The Standard Model: Read PDF
pp. 9-28
3 - Phenomenology of the Standard Model: Read PDF
pp. 29-62
4 - The Standard Model as an effective field theory: Read PDF
pp. 63-74
5 - Anomalies, instantons and the strong CP problem: Read PDF
pp. 75-106
6 - Grand unification: Read PDF
pp. 107-118
7 - Magnetic monopoles and solitons: Read PDF
pp. 119-130
8 - Technicolor: a first attempt to explain hierarchies: Read PDF
pp. 131-136
Part 2 - Supersymmetry: Read PDF
pp. 137-138
pp. 139-156
10 - A first look at supersymmetry breaking: Read PDF
pp. 157-166
11 - The Minimal Supersymmetric Standard Model: Read PDF
pp. 167-184
12 - Supersymmetric grand unification: Read PDF
pp. 185-190
13 - Supersymmetric dynamics: Read PDF
pp. 191-208
14 - Dynamical supersymmetry breaking: Read PDF
pp. 209-218
15 - Theories with more than four conserved supercharges: Read PDF
pp. 219-232
16 - More supersymmetric dynamics: Read PDF
pp. 233-242
17 - An introduction to general relativity: Read PDF
pp. 243-258
pp. 259-268
19 - Astroparticle physics and inflation: Read PDF
pp. 269-302
Part 3 - String theory: Read PDF
pp. 303-304
pp. 305-312
21 - The bosonic string: Read PDF
pp. 313-340
22 - The superstring: Read PDF
pp. 341-358
23 - The heterotic string: Read PDF
pp. 359-364
24 - Effective actions in ten dimensions: Read PDF
pp. 365-372
25 - Compactification of string theory I. Tori and orbifolds: Read PDF
pp. 373-400
26 - Compactification of string theory II. Calabi–Yau compactifications: Read PDF
pp. 401-428
27 - Dynamics of string theory at weak coupling: Read PDF
pp. 429-440
28 - Beyond weak coupling: non-perturbative string theory: Read PDF
pp. 441-466
29 - Large and warped extra dimensions: Read PDF
pp. 467-474
30 - Coda: where are we headed?: Read PDF
pp. 475-480
Part 4 - The appendices: Read PDF
pp. 481-482
Appendix A - Two-component spinors: Read PDF
pp. 483-486
Appendix B - Goldstone's theorem and the pi mesons: Read PDF
pp. 487-490
Appendix C - Some practice with the path integral in field theory: Read PDF
pp. 491-500
Appendix D - The beta function in supersymmetric Yang–Mills theory: Read PDF
pp. 501-504
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