arXiv subjects

J. C. Pérez Bueno

Publications and source records attributed to J. C. Pérez Bueno.

6 recordsLinked to original sources

arXiv1999

The geometry of branes and extended superspaces

We argue that a description of supersymmetric extended objects from a unified geometric point of view requires an enlargement of superspace. To this aim we study in a systematic way how superspace groups and algebras arise from Grassmann spinors when these are assumed to be the only primary entities. In the process, we recover generalized spacetime superalgebras and extensions of supersymmetry found earlier. The enlargement of ordinary superspace with new parameters gives rise to extended superspace groups, on which manifestly supersymmetric actions may be constructed for various types of p-branes, including D-branes (given by Chevalley-Eilenberg cocycles) with their Born-Infeld fields. This results in a field/extended superspace democracy for superbranes: all brane fields appear as pull-backs from a suitable target superspace. Our approach also clarifies some facts concerning the origin of the central charges for the different p-branes.

hep-th↗

arXiv1998

Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.

math-ph↗

arXiv1996

Geometrical foundations of fractional supersymmetry

A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When $q$ is a root of unity the algebra is found to have a non-trivial Hopf structure, extending that associated with the anyonic line. One-dimensional ordinary/fractional superspace is identified with the braided line when $q$ is a root of unity, so that one-dimensional ordinary/fractional supersymmetry can be viewed as invariance under translation along this line. In our construction of fractional supersymmetry the $q$-deformed bosons play a role exactly analogous to that of the fermions in the familiar supersymmetric case.

hep-th↗

arXiv1996

Braided structure of fractional $Z_3$-supersymmetry

It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2πi/3)$ 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 $q\to\exp(2πi/3)$ limits of the left and right derivatives from the calculus on the braided line

hep-th↗

arXiv1996

The $q$-calculus for generic $q$ and $q$ a root of unity

The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${\cal Z}_n$-graded fractional supersymmetry and its natural representation.

q-alg↗

arXiv1996

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.

hep-th↗