274 research outputs found
Superbranes, D=11 CJS supergravity and enlarged superspace coordinates/fields correspondence
We discuss the r\^ole of enlarged superspaces in two seemingly different
contexts, the structure of the -brane actions and that of the
Cremmer-Julia-Scherk eleven-dimensional supergravity. Both provide examples of
a common principle: the existence of an {\it enlarged superspaces
coordinates/fields correspondence} by which all the (worldvolume or spacetime)
fields of the theory are associated to coordinates of enlarged superspaces. In
the context of -branes, enlarged superspaces may be used to construct
manifestly supersymmetry-invariant Wess-Zumino terms and as a way of expressing
the Born-Infeld worldvolume fields of D-branes and the worldvolume M5-brane
two-form in terms of fields associated to the coordinates of these enlarged
superspaces. This is tantamount to saying that the Born-Infeld fields have a
superspace origin, as do the other worldvolume fields, and that they have a
composite structure. In =11 supergravity theory enlarged superspaces arise
when its underlying gauge structure is investigated and, as a result, the
composite nature of the field is revealed: there is a full one-parametric
family of enlarged superspace groups that solve the problem of expressing
in terms of spacetime fields associated to their coordinates. The corresponding
enlarged supersymmetry algebras turn out to be deformations of an {\it
expansion} of the algebra. The unifying mathematical structure
underlying all these facts is the cohomology of the supersymmetry algebras
involved.Comment: plain latex, 29 pages, no figures. To appear in the Am. Inst. of
Phys. Proc. Serie
Central extensions, classical non-equivariant maps and residual symmetries
The arising of central extensions is discussed in two contexts. At first
classical counterparts of quantum anomalies (deserving being named as
"classical anomalies") are associated with a peculiar subclass of the
non-equivariant maps. Further, the notion of "residual symmetry" for theories
formulated in given non-vanishing EM backgrounds is introduced. It is pointed
out that this is a Lie-algebraic, model-independent, concept.Comment: 8 pages, LaTex. Talk given at the International Conference
"Renormalization Group and Anomalies in Gravitation and Cosmology", Ouro
Preto, Brazil, March 2003. To appear in the Proceeding
Minimal D=4 supergravity from the superMaxwell algebra
We show that the first-order D=4, N=1 pure supergravity lagrangian four-form
can be obtained geometrically as a quadratic expression in the curvatures of
the Maxwell superalgebra. This is achieved by noticing that the relative
coefficient between the two terms of the Lagrangian that makes the action
locally supersymmetric also determines trivial field equations for the gauge
fields associated with the extra generators of the Maxwell superalgebra. Along
the way, a convenient geometric procedure to check the local supersymmetry of a
class of lagrangians is developed.Comment: Plain latex, 14 pages. Two misprints corrected, one reference adde
n-ary algebras: a review with applications
This paper reviews the properties and applications of certain n-ary
generalizations of Lie algebras in a self-contained and unified way. These
generalizations are algebraic structures in which the two entries Lie bracket
has been replaced by a bracket with n entries. Each type of n-ary bracket
satisfies a specific characteristic identity which plays the r\^ole of the
Jacobi identity for Lie algebras. Particular attention will be paid to
generalized Lie algebras, which are defined by even multibrackets obtained by
antisymmetrizing the associative products of its n components and that satisfy
the generalized Jacobi identity (GJI), and to Filippov (or n-Lie) algebras,
which are defined by fully antisymmetric n-brackets that satisfy the Filippov
identity (FI). Three-Lie algebras have surfaced recently in multi-brane theory
in the context of the Bagger-Lambert-Gustavsson model. Because of this,
Filippov algebras will be discussed at length, including the cohomology
complexes that govern their central extensions and their deformations
(Whitehead's lemma extends to all semisimple n-Lie algebras). When the
skewsymmetry of the n-Lie algebra is relaxed, one is led the n-Leibniz
algebras. These will be discussed as well, since they underlie the
cohomological properties of n-Lie algebras.
The standard Poisson structure may also be extended to the n-ary case. We
shall review here the even generalized Poisson structures, whose GJI reproduces
the pattern of the generalized Lie algebras, and the Nambu-Poisson structures,
which satisfy the FI and determine Filippov algebras. Finally, the recent work
of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be
briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra
structure and on why the A_4 model may be formulated in terms of an ordinary
Lie algebra, and on its Nambu bracket generalization.Comment: Invited topical review for JPA Math.Theor. v2: minor changes,
references added. 120 pages, 318 reference
Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms
By means of a generalization of the Maurer-Cartan expansion method we
construct a procedure to obtain expanded higher-order Lie algebras. The
expanded higher order Maurer-Cartan equations for the case
are found. A dual formulation for the
S-expansion multialgebra procedure is also considered. The expanded higher
order Maurer Cartan equations are recovered from S-expansion formalism by
choosing a special semigroup. This dual method could be useful in finding a
generalization to the case of a generalized free differential algebra, which
may be relevant for physical applications in, e.g., higher-spin gauge theories
Contractions, Hopf algebra extensions and cov. differential calculus
We re-examine all the contractions related with the
deformed algebra and study the consequences that the contraction process has
for their structure. We also show using
as an example that, as in the undeformed case, the contraction may generate
Hopf algebra cohomology. We shall show that most of the different Hopf algebra
deformations obtained have a bicrossproduct or a cocycle bicrossproduct
structure, for which we shall also give their dual `group' versions. The
bicovariant differential calculi on the deformed spaces associated with the
contracted algebras and the requirements for their existence are examined as
well.Comment: TeX file, 25 pages. Macros are include
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