Codimension one branes

Abstract

We study codimension one branes, i.e. p-branes in (p + 2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p = 1, 2, 3, 5, 9. For p = 3, 5, 9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose generalised field strength obeys a constraint deducible from considering an open supermembrane ending on the p-brane. This constraint, together with the embedding constraint, puts the system on-shell for p = 5 but overconstrains the 9-brane in D = 11 such that the Goldstone superfield is frozen. For p = 3 these two constraints give rise to an off-shell linear multiplet on the worldvolume. An alternative formulation of this case is given in which the linear multiplet is dualised to an off-shell scalar multiplet. Actions are constructed for both cases and are shown to give equivalent equations of motion. After gauge fixing a local Sp(1) symmetry associated with shifts in the Sp(1) R Goldstone modes, we find that the auxiliary fields in the scalar multiplet parametrise a two-sphere. For completeness we also discuss briefly the cases p = 1, 2 where the equations of motion (for off-shell multiplets) are obtained from an action principle.

Codimension zero superembeddings

“…In other words, h transforms projectively under G. This symmetry was discussed for the 3-brane in six dimensions in [6]; it can be used to choose different gauges for E α α .…”

“…Alternatively, one can impose further constraints directly on the superembedding which are equivalent to the F-constraint, but it is simpler to impose the latter directly as it is unambiguous. An example of this is given by the 5-brane in D = 7 for which the equations were obtained by an additional geometrical constraint in [7] and then by the F-constraint in [6].…”

Heterotic kink solitons and their worldvolume action

“…As in the AdS case [12], we find that, in addition to the DBI term, there are three higher-derivative contributions. These are proportional toK,R (4) andK 2 , whereK,R (4) are the trace of the extrinsic curvature and the intrinsic scalar curvature respectively. The coefficients of these terms, as well as the overall "brane tension", depend on three parameters-the width of the kink, l, the warp, δ, and the location of the boundary walls, u 0 .…”

“…The result is expressed in terms of the trace of the extrinsic curvature and the intrinsic curvature scalar.There has been considerable interest in calculating the worldvolume effective action of topological solitons in various contexts. The lowest order Dirac-Born-Infeld (DBI) term was given for differing theories in [1][2][3][4][5][6][7][8][9]. In [10,11], Gregory and collaborators presented a compelling formalism for computing higher-order corrections to the action of co-dimension one scalar "kink" solitons in the "probe brane" limit.…”

New Superembeddings for Type II Superstrings

“…Superembedding approach treatment for these superbranes was performed e.g. in [32], [33], [43].) On the other hand, for on-shell embeddings the basic superembedding equation encompasses full information about the superbrane dynamics.…”