[Article] Introduction To Supersymetry

[Article] Introduction To Supersymetry -...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
arXiv:hep-th/9612114v1 11 Dec 1996 FERMILAB-PUB-96/445-T INTRODUCTION TO SUPERSYMMETRY JOSEPH D. LYKKEN Fermi National Accelerator Laboratory P.O. Box 500 Batavia, IL 60510 These lectures give a self-contained introduction to supersymmetry from a modern perspective. Emphasis is placed on material essential to understanding duality. Topics include: central charges and BPS-saturated states, supersymmetric nonlin- ear sigma models, N=2 Yang-Mills theory, holomorphy and the N=2 Yang-Mills β function, supersymmetry in 2, 6, 10, and 11 spacetime dimensions. 1 Introduction “Never mind, lads. Same time tomorrow. We must get a winner one day.” – Peter Cook, as the doomsday prophet in “The End of the World”. Supersymmetry, along with its monozygotic sibling superstring theory, has become the dominant framework for formulating physics beyond the standard model. This despite the fact that, as of this morning, there is no unambiguous experimental evidence for either idea. Theorists find supersymmetry appealing for reasons which are both phenomenological and technical. In these lectures I will focus exclusively on the technical appeal. There are many good recent re- views of the phenomenology of supersymmetry. 1 Some good technical reviews are Wess and Bagger, 2 West, 3 and Sohnius. 4 The goal of these lectures is to provide the student with the technical back- ground requisite for the recent applications of duality ideas to supersymmetric gauge theories and superstrings. More specifically, if you absorb the material in these lectures, you will understand Section 2 of Seiberg and Witten, 5 and you will have a vague notion of why there might be such a thing as M -theory. Beyond that, you’re on your own. 2 Representations of Supersymmetry 2.1 The general 4-dimensional supersymmetry algebra A symmetry of the S-matrix means that the symmetry transformations have the effect of merely reshuffling the asymptotic single and multiparticle states. The known symmetries of the S-matrix in particle physics are: 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Poincar´ e invariance, the semi-direct product of translations and Lorentz rotations, with generators P m , M mn . So-called “internal” global symmetries, related to conserved quantum numbers such as electric charge and isospin. The symmetry generators are Lorentz scalars and generate a Lie algebra, [ B ,B k ] = iC j ℓk B j , (1) where the C j ℓk are structure constants. Discrete symmetries: C, P, and T. In 1967, Coleman and Mandula 6 provided a rigorous argument which proves that, given certain assumptions, the above are the only possible sym- metries of the S-matrix. The reader is encouraged to study this classic paper and think about the physical and technical assumptions which are made there. The Coleman-Mandula theorem can be evaded by weakening one or more of its assumptions. In particular, the theorem assumes that the symmetry alge- bra of the S-matrix involves only commutators. Weakening this assumption to allow anticommuting generators as well as commuting generators leads to the possibility of supersymmetry . Supersymmetry (or SUSY for short) is defined
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern