By A. S. Galperin
By E. A. Ivanov
By V. I. Ogievetsky
By E. S. Sokatchev
Publisher: Cambridge University Press
Print Publication Year: 2001
Online Publication Date:August 2009
Online ISBN:9780511535109
Hardback ISBN:9780521801645
Paperback ISBN:9780521020428
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535109.014
Subjects: Theoretical Physics and Mathematical Physics, Mathematical physics
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We have presented the basics of the harmonic superspace approach but not the latest developments. Some of the most recent are mentioned in the Introduction as the motivation for writing this book. During the past few years this method has been advanced in several directions, some of which we briefly overview here.
Firstly, even at the early stages it was realized that higher N supersymmetries provide many more possibilities for choosing the harmonic superspaces and their analytic subspaces due to the higher rank of the relevant R symmetry groups. In [17] an exhaustive list of the coset spaces of such groups in terms of the corresponding harmonic variables was presented. No a priori reasons exist for preferring any of these higher N harmonic superspaces and the right choice is imposed by the problem at hand. For instance, as we have seen, the problem of constructing an off-shell formulation of N = 3 super Yang-Mills theory (which coincides with N = 4 SYM on shell) is solved using an N = 3 harmonic superspace based on the coset SU (3) / U (1) × U (1) [G5, G6]. Unfortunately, the analogous problem in N = 4 has not yet been solved. The only recent development has been the harmonic superspace (based upon the coset SU (4) / SU (2) × SU (2) × U (1)) reformulation of the on-shell constraints of N = 4 SYM proposed in [H19, H21].
pp. i-vi
pp. vii-xii
pp. xiii-xiv
1 - Introductory overview : Read PDF
pp. 1-26
2 - Elements of supersymmetry : Read PDF
pp. 27-43
pp. 44-65
4 - Harmonic analysis : Read PDF
pp. 66-73
5 - N = 2 matter with infinite sets of auxiliary fields : Read PDF
pp. 74-106
6 - N = 2 matter multiplets with a finite number of auxiliary fields. N = 2 duality transformations : Read PDF
pp. 107-127
7 - Supersymmetric Yang–Mills theories : Read PDF
pp. 128-147
8 - Harmonic supergraphs : Read PDF
pp. 148-174
9 - Conformal invariance in N = 2 harmonic superspace : Read PDF
pp. 175-188
pp. 189-216
11 - Hyper-Kähler geometry in harmonic space : Read PDF
pp. 217-262
12 - N = 3 supersymmetric Yang–Mills theory : Read PDF
pp. 263-280
pp. 281-282
Appendix: Notations, conventions and useful formulas : Read PDF
pp. 283-288
pp. 289-303
pp. 304-306