PREPARED FOR SUBMISSION TO JHEP BUSSTEPP lectures on Supersymmetry Stephen M. West Royal Holloway, University of London Egham, Surrey, TW20 0EX E-mail: Stephen. West@rhul. ac. uk ABSTRACT: These lecture notes accompany the Supersymmetry lectures delivered at BUSSTEPP in 2014. They cover a basic introduction to supersymmetry with a detailed description of how to construct a supersymmetric action.
Contents 1 Books and references 2 2 Conventions 2 3 The Gauge Hierarchy Problem and the motivation for Supersymmetry. 3 4 Supersymmetry Algebra and Representations 4 4.1 Poincaré symmetry and Spinors 4 4.2 Supersymmetry algebra 6 5 Superspace and Superfields 11 5.1 Chiral Superfields 14 5.2 Vector Superfields 19 5.2.1 Non-abelian gauge symmetry 22 5.2.2 Abelian vector superfield Lagrangian. 23 5.2.3 Non-abelian vector superfield Lagrangian. 25 5.3 R-Symmetry 26 6 The MSSM 28 7 Breaking Supersymmetry 31 8 F- and D-term Breaking. 32 8.1 F-Breaking 34 8.2 D-term or Fayet-Illiopoulos Breaking 37 - 1 - A Spinor Manipulation 39 B Superfields 43
1 Books and references Much of these lecture notes are derived from books, reviews and other lectures. A partial list accompanied by other useful references are . S. P. Martin, A Supersymmetry primer; hep-ph/9709356 . I. J. R. Aitchison, Supersymmetry and the MSSM: An Elementary Introduction, hep-ph/0505105v1 . J. Wess, J. Bagger, Supersymmetry and Supergravity, Princeton University Press, (1992). · H. Baer, X. Tata; Weak Scale Supersymmetry; CUP (2006) · P. Binétruy, Supersymmetry, OUP (2008) · J. D. Lykken, "Introduction to supersymmetry," hep-th/9612114. . F. Quevedo, S. Krippendorf and O. SchlottererCambridge Lectures on Supersym- metry and Extra Dimensions, Cambridge Lectures on Supersymmetry and Extra Dimensions, arXiv:1011.1491 [hep-th]. Further reading ... . M. A. Luty, 2004 TASI lectures on supersymmetry breaking, hep-th/0509029. . J. Terning, TASI 2002 lectures: Non-perturbative supersymmetry, hep-th/0306119. Warning: Although I have made every effort to make these notes consistent and correct, minus signs and factors of 2 are notoriously difficult to get right in supersymmetry. I urge the reader to check results presented in these notes carefully and I apologies in advance for the inevitable inclusion of typos and stupid errors. 2 Conventions Before we start, it is worth establishing some notation. In these notes I will use the mostly negative metric, nuV = diag(+,-,-,-). In addition we use the following representation of the gamma matrices ! 2H = µ 0 where 0 gH , 75 = ? ! -10 0 1 ' (2.1) ! 10 ! o2 = - 02 = 0 -i i 0 , ! 01 = - 01 = 01 ? 6 01 , 03 -03. 10 ' ! 1 0 0 -1 ' (2.2) - 2 - ----