Hidden supersymmetries in supersymmetric quantum mechanics

We discuss the appearance of additional, hidden supersymmetries for simple 0+1 $Ad(G)$-invariant supersymmetric models and analyse some geometrical mechanisms that lead to them. It is shown that their existence depends crucially on the availability of odd order invariant skewsymmetric tensors on the (generic) compact Lie algebra $\cal G$, and hence on the cohomology properties of the Lie algebra considered.Comment: Misprints corrected, two refs. added. To appear in NP

On the general structure of gauged Wess-Zumino-Witten terms

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit general expression for these cocycles is given. The common geometrical structure of the gauged closed forms and the D'Hoker and Weinberg effective actions of WZW type, as well as the obstructions for their existence, is also exhibited and explained.Comment: Some changes. 23 pages; latex2e file. To appear in Nucl. Phys.

Invariant tensors for simple groups

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.Comment: Latex file. 34 pages. (Trivial) misprints corrected. To appear in Nucl. Phys.

Braided structure of fractional Z3Z_3-supersymmetry

It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2\pi i/3)$ limit of the braided line. $Z_3$-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its associated covariant derivative emerge as the $q\to\exp(2\pi i/3)$ limits of the left and right derivatives from the calculus on the braided lineComment: 8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium `Quantum groups and integrable systems', Prague, June 1996 (to appear in Czech. J. Phys.

On the underlying gauge group structure of D=11 supergravity

The underlying gauge group structure of D=11 supergravity is revisited (see paper for detailed abstract).Comment: 16 pages, no figure

Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations

This paper deals with the striking fact that there is an essentially canonical path from the $i$-th Lie algebra cohomology cocycle, $i=1,2,... l$, of a simple compact Lie algebra \g of rank $l$ to the definition of its primitive Casimir operators $C^{(i)}$ of order $m_i$. Thus one obtains a complete set of Racah-Casimir operators $C^{(i)}$ for each \g and nothing else. The paper then goes on to develop a general formula for the eigenvalue $c^{(i)}$ of each $C^{(i)}$ valid for any representation of \g, and thereby to relate $c^{(i)}$ to a suitably defined generalised Dynkin index. The form of the formula for $c^{(i)}$ for $su(n)$ is known sufficiently explicitly to make clear some interesting and important features. For the purposes of illustration, detailed results are displayed for some classes of representation of $su(n)$, including all the fundamental ones and the adjoint representation.Comment: Latex, 16 page

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German

Supersymmetry from a braided point of view

We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and covariant derivative are obtained in the limit in question as the left and right derivatives of the calculus on the braided line.Comment: LateX file. 10 pages. To appear in Phys. Lett.

(p,q) D=3 Poincare supergravities from Lie algebra expansions

We use the expansion of superalgebras procedure (summarized in the text) to derive Chern-Simons (CS) actions for the (p,q)-Poincare supergravities in three-dimensional spacetime. After deriving the action for the (p,0)-Poincare supergravity as a CS theory for the expansion osp(p|2;R)(2,1) of osp(p|2;R), we find the general (p,q)-Poincare superalgebras and their associated D=3 supergravity actions as CS gauge theories from an expansion of the simple osp(p+q|2,R) superalgebras, namely osp(p+q|2,R)(2,1,2).Comment: v2: two references added, 17 pages. To appear in NP

Supergravity interacting with bosonic p-branes and local supersymmetry

We study the coupling of supergravity with a purely bosonic brane source (bosonic p-brane). The interaction, described by the sum of their respective actions, is self-consistent if the bosonic p-brane is the pure bosonic limit of a super-p-brane. In that case the dynamical system preserves 1/2 of the local supersymmetry characteristic of the `free' supergravity.Comment: 11 pages, RevTe