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

Abstract

We discuss the rôle of enlarged superspaces in two seemingly different contexts, the structure of the p-brane actions and that of the Cremmer-Julia-Scherk elevendimensional supergravity. Both provide examples of a common principle: the existence of an 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 p-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 D=11 supergravity theory enlarged superspaces arise when its underlying gauge structure is investigated and, as a result, the composite nature of the A 3 field is revealed: there is a full one-parametric family of enlarged superspace groups that solve the problem of expressing A 3 in terms of spacetime fields associated to their coordinates. The corresponding enlarged supersymmetry algebras turn out to be deformations of an expansion of the osp(1|32) algebra. The unifying mathematical structure underlying all these facts is the cohomology of the supersymmetry algebras involved.

Expanding Lie (super)algebras through Abelian semigroups

“…This vantage viewpoint may help better understand fundamental problems related to the geometrical formulation of 11-dimensional Supergravity. Some physical applications of the expansion procedure have been developed in [6,7,8,9,10,11,12,13,14].…”

Polyvector Super-Poincaré Algebras, M, F Theory Algebras and Generalized Supersymmetry in Clifford-Spaces

“…For example, one has to verify that the graded Jacobi identities are satisfied ( nontrivial task ). Thirdly, one must find what the enlarged polyvector superspaces look like, which are very different than the tensorial superspaces described in [10] . We will discuss these issues in the next section.…”

“…One can notice that a string propagating in the latter dimensions, has for transverse degrees of freedom D − 2 = 1, 2, 4, 8 which precisely match the degrees of freedom of the real, complex, quaternion and octonion normed-division algebras . The role of enlarged superspace coordinates in the context of super p-branes, Born-Infeld and M-theory has recently been investigated by [10] . Clifford Spaces are more f undamental than these tensorial spaces ( have a richer structure ) because they require polyvector coordinates ( antisymmetric tensors) of variable rank ( greater than two ) until saturating the values of the spacetime dimensions.…”

On the underlyingE11symmetry of theD= 11 free differential algebra

“…In particular, the corresponding expansion of C (2.45) gives the general structure for a candidate superfivebrane Wess-Zumino term in flat background. In fact, as discussed in [25], the problem of reducing a minimal FDA to an ordinary algebra is mathematically equivalent to that of obtaining strictly invariant Wess-Zumino terms from the originally quasi-invariant ones. In [26,27,28], strictly invariant Wess-Zumino terms were proposed; as they include the generators Σ αβ they are not suitable to describe the minimal D = 11 FDA, for which R ab = 0 .…”

“…This corresponds to the statement that (2.16) is an algebra equivalent to the FDA (2.12)-(2.14) [13]. The groupG 0 corresponding to the FDA (2.12)-(2.14) may be not unique [25].…”