The geometry of branes and extended superspaces

Abstract

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.Comment: Latex file, 31 pgs. Version to appear in NP

Expansions of Algebras and Superalgebras and Some Applications

“…Examples of extensions in physics are the centrally extended Galilei algebra, which is relevant in non-relativistic quantum mechanics (and that may be obtanined as a contraction of the trivially extended D = 4 Poincaré group, see [42] to see how contractions may generate cohomology), the two-dimensional extended Poincaré algebra that allows [43] for a gauge theoretical derivation of the Callan-Giddings-Harvey-Strominger model [44] for twodimensional gravity, or the M-theory superalgebra that, without its Lorentz automorphisms part, is the maximal central extension of the abelian D = 11 supertranslations algebra ( [8,9,5,12]). …”

“…namely, when 12) are satisfied through those for G. This is a consequence of the fact that, for G, the exterior derivative of the λ-expansion of the MC equations is the λ-expansion of their exterior derivative, but it may also be seen directly.…”

“…The worldvolume BI fields, as the spacetime A 3 field of CJS supergravity above, become composite fields. Moreover, a Chevalley-Eilenberg Lie algebra cohomology analysis [57,12,58] of the Wess-Zumino terms of many different superbrane actions determines the possible ones and how the ordinary supersymme-try algebra has to be extended (see also [56,59]). This again suggests an enlarged superspace variables/worldvolume fields correspondence.…”

Superbranes, D = 11 CJS Supergravity and Enlarged Superspace Coordinates/Fields Correspondence

“…The relation between semi-or quasi-invariance (i.e., invariance but for a total derivative) of lagrangians, cohomology and group extension theory, is a problem which has a fifty years long history, but we will not discuss it here (see [27] and references therein). In the case of p-branes, the additional variables of the new supersymetry groups [22] (rigid enlarged superspaces) appear in these manifestly invariant WZ terms in a trivial way, but this is not the case for all types of branes. It was shown in [22] that the enlarged superspaces, could also be used to obtain Born-Infeld (BI) fields from one-forms defined on them (for BI fields in the IIB case see [28]).…”

“…This is why is more precise to speak of a correspondence between (enlarged superspace) coordinates and fields rather than of 'democracy' -the term used in [22]-since its original use referred to a democracy between the fields and its arguments. We have conjectured [22] the existence of a correspondence between the coordinates of a suitable superspace and the fields in theory constructed on it. These appear as the pullbacks of forms, originally defined on the target enlarged superspace, to the worldvolume or spacetime manifolds.…”