367 research outputs found
Hidden supersymmetries in supersymmetric quantum mechanics
We discuss the appearance of additional, hidden supersymmetries for simple
0+1 -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 , and hence on the cohomology
properties of the Lie algebra considered.Comment: Misprints corrected, two refs. added. To appear in NP
Membranes and Consistent Quantization of Nambu Dynamics
The dynamics of even topological open membranes relies on Nambu Brackets.
Consequently, such 2p-branes can be quantized through the consistent
quantization of the underlying Nambu dynamical structures. This is a summary
construction relying on the methods detailed in refs hep-th/0205063 and
hep-th/0212267.Comment: LaTeX2e, 8 pages, 1 figure. Invited talk at the 8th International
Wigner Symposium, 26-30 May 2003, New York, SPIRES Conf C03/05/2
Wess-Zumino terms for AdS D-branes
We show that Wess-Zumino terms for D-p branes with p>0 in the Anti-de Sitter
(AdS) space are given in terms of "left-invariant" currents on the super-AdS
group or the "expanded" super-AdS group. As a result there is no topological
extension of the super-AdS algebra. In the flat limit the global Lorentz
rotational charges of the AdS space turn out to be brane charges of the
supertranslation algebra representing the BPS mass. We also show that a
D-instanton is described by the GL(1) degree of freedom in the Roiban-Siegel
formalism based on the GL(4|4)/[Sp(4)xGL(1)]^2 coset.Comment: 17 pages, references and comment added, Version to appear in Nucl.
Phys.
Compilation of relations for the antisymmetric tensors defined by the Lie algebra cocycles of
This paper attempts to provide a comprehensive compilation of results, many
new here, involving the invariant totally antisymmetric tensors (Omega tensors)
which define the Lie algebra cohomology cocycles of , and that play an
essential role in the optimal definition of Racah-Casimir operators of .
Since the Omega tensors occur naturally within the algebra of totally
antisymmetrised products of -matrices of , relations within
this algebra are studied in detail, and then employed to provide a powerful
means of deriving important Omega tensor/cocycle identities. The results
include formulas for the squares of all the Omega tensors of . Various
key derivations are given to illustrate the methods employed.Comment: Latex file (run thrice). Misprints corrected, Refs. updated.
Published in IJMPA 16, 1377-1405 (2001
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.
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
Topics on n-ary algebras
We describe the basic properties of two n-ary algebras, the Generalized Lie
Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and
comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and
Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology
relevant for the central extensions and infinitesimal deformations of FAs. It
is seen that semisimple FAs do not admit central extensions and, moreover, that
they are rigid. This extends the familiar Whitehead's lemma to all
FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is
no longer required to be fully skewsymmetric one is led to the n-Leibniz (or
Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz
algebras, those with an anticommutative n-bracket, we study the class of
n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first
n-1 entires of the n-Leibniz bracket.Comment: 11 page
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