Introduction to supersymmetry

por Evgeny Ivanov (Bogoliubov Laboratory of Theoretical Physics)

martes 2 may. 2006 15:00 → 16:00 Europe/Madrid

Sala Seminarios (Dpto. de Física Teórica (UVEG))

beginning 2nd May 2006 and lasting two weeks (timetable: May 2,3,4: 15.00-17.30; May 8: 11.00-13.00; May 9,10,11: 15.00-17.30) Plan of the course (tentative) 1. Simple and extended Poincaré supersymmetry: motivations, definitions, notation. The no-go Coleman-Mandula theorem and how it is evaded in extended susy. 4D-susy via dimensional reduction from D > 4; central charges. Examples of susy realizations on fields: physical and auxiliary fields, on-shell and off-shell realizations. Non-linear realizations of spontaneously broken supersymmetry. 2. Superspace as a natural framework for supersymmetry. Coset approach. Merits of off-shell superfield formulations. Superspin as a generalization of the square of Pauli-Lubanski vector. Chirality as the simplest Grassmann analyticity. N=1 theories in superspace: matter and super Yang-Mills. Kähler geometry of N=1 sigma models from their superspace formulation. 3. N=2 supersymmetry and harmonic superspace. Grassmann harmonic analyticity as the true N=2 analog of N=1 chirality. N=2 hypermultiplet on shell and off shell, infinite number of auxiliary fields as the price for off-shell unconstrained formulation. Most general hypermultiplet action and hyper Kähler sigma models. 4. Geometric principles underlying N=0 and N=1 gauge theories. N=2 SYM theory from preserving harmonic analyticity. Wess-Zumino gauge in N=1 and N=2 supersymmetric Yang Mills (SYM) theories. Superfield and component actions. Maximally extended N=4 SYM theory in N=2 superfield formulation. 5. Elements of quantum superfield theory. Fixing the gauge, superfield FP ghosts, vertices and propagators. Simplest Feynman supergraphs. Basic idea of non-renormalization theorems. 6. Supergravity as supersymmetrization of Einstein theory. Questions to be answered. N=1 supergravity, the method of conformal compensators. From conformal N=2 SG to N=2 Poincaré SG. Maximally extended N=8 SG. 7. N=3 harmonic analyticity. The N=3 SYM off-shell action as the harmonic analogue of Chern-Simons action. Ultraviolet finiteness made manifest. 8. Some instructive toy examples. N=2, N=4 and N=8 supersymmetric mechanics. N=4, 1D harmonic superspace. Gauging supersymmetric quantum mechanics as a tool to relate its various models (based on some recent work). 9. Some uses of superconformal symmetries in diverse dimensions. Conformal/AdS superalgebras. A simple example: conformal and superconformal mechanics. Tensorial superspace and its generalized superconformal symmetry OSp(1|8). Higher spins from non-linear realizations of OSp(1|8).