Supersymmetric Mechanics in Superspace

Abstract

These Lectures have been given at Laboratori Nazionali di Frascati in the month of March, 2005. The main idea was to provide our young collegues, who joined us in our attempts to understand the structure of $N$-extended supersymmetric one-dimensional systems, with short descriptions of the methods and techniques we use. This was reflected in the choice of material and in the style of presentation. We base our treatment mainly on the superfield point of view. Moreover, we prefer to deal with N=4 and N=8 superfields. At present, the exists an extensive literature on the components approach to extended supersymmetric theories in $d=1$ while the manifestly supersymmetric formulation in terms of properly constrained superfields is much less known. Nevertheless, we believe that just such formulations are preferable. In order to make these Lectures more or less self-consistent, we started from the simplest examples of one-dimensional supersymmetric theories and paid a lot of attention to the peculiarities of $d=1$ supersymmetry. From time to time we presented the calculations in a very detailed way. In other cases we omitted the details and gave only the final answers. In any case these Lectures cannot be considered as a textbook in any respect. They can be considered as our personal point of view on the one-dimensional superfield theories and on the methods and techniques we believe to be important. Especially, all this concerns Section 3, were we discuss the nonlinear realizations method. We did not present any proofs in this Section. Instead we focused on the details of calculations. Finally, we apologize for the absolutely incomplete list of References.

References in corpus (3)

• ABC of N=8, d=1 supermultiplets
• N=8 supersymmetric mechanics on special Kähler manifolds
• N=4 supersymmetric mechanics with nonlinear chiral supermultiplet

Cited by in corpus (20)

• 4D, N = 1 Supersymmetry Genomics (I)
• Nonlinear realizations of symmetries and unphysical Goldstone bosons
• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Potentials in N=4 superconformal mechanics
• N=4 superconformal n-particle mechanics via superspace
• Biharmonic Superspace for N=4 Mechanics
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• Superfield Formulation of Nonlinear N=4 Supermultiplets
• A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• ${\mathbb{Z}}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
• Partial breaking of global supersymmetry and super particle actions
• Super 0--brane action on the coset space of $D(2,1;\alpha )$ supergroup
• Dual multiplets in N=4 superconformal mechanics
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• On $OSp(N|2)$ superconformal mechanics
• N=8 supersymmetric mechanics on the sphere S^3
• Supersymmetric higher-derivative models in quantum cosmology