BRS Cohomology of the Supertranslations in D=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $\delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag}$. We find that the cohomology of this operator depends on a spin-orbit coupling in an SU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9

Topics on the geometry of D-brane charges and Ramond-Ramond fields

In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called *-problem and make some brief remarks about it.Comment: 29 pages, no figure

Towards reduction of type II theories on SU(3) structure manifolds

We revisit the reduction of type II supergravity on SU(3) structure manifolds, conjectured to lead to gauged N=2 supergravity in 4 dimensions. The reduction proceeds by expanding the invariant 2- and 3-forms of the SU(3) structure as well as the gauge potentials of the type II theory in the same set of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions. By focussing on the metric sector, we arrive at a list of constraints these expansion forms should satisfy to yield a base point independent reduction. Identifying these constraints is a first step towards a first-principles reduction of type II on SU(3) structure manifolds.Comment: 20 pages; v2: condition (2.13old) on expansion forms weakened, replaced by (2.13new), (2.14new

The general (2,2) gauged sigma model with three--form flux

We find the conditions under which a Riemannian manifold equipped with a closed three-form and a vector field define an on--shell N=(2,2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized Kaehler structure, that the vector field preserves this structure, and that a so--called generalized moment map exists for it. By a theorem in generalized complex geometry, these conditions imply that the quotient is again a twisted generalized Kaehler manifold; this is in perfect agreement with expectations from the renormalization group flow. This method can produce new N=(2,2) models with NS flux, extending the usual Kaehler quotient construction based on Kaehler gauged sigma models.Comment: 24 pages. v2: typos fixed, other minor correction

Dynamic SU(2) Structure from Seven-branes

We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.Comment: 49 pages, 2 figures; v2: minor corrections, references adde

Relating branes and matrices

We construct a general map between a Dp-brane with magnetic flux and a matrix configuration of D0-branes, by showing how one can rewrite the boundary state of the Dp-brane in terms of its D0-brane constituents. This map gives a simple prescription for constructing the matrices of fuzzy spaces corresponding to branes of arbitrary shape and topology. Since we explicitly identify the D0-brane degrees of freedom on the brane, we also derive the D0-brane charge of the brane in a very direct way including the A-genus term. As a check on our formalism, we use our map to derive the abelian-Born-Infeld equations of motion from the action of the D0-brane matrices.Comment: 28 pages, Late

D-brane charges on non-simply connected groups

The maximally symmetric D-branes of string theory on the non-simply connected Lie group SU(n)/Z_d are analysed using conformal field theory methods, and their charges are determined. Unlike the well understood case for simply connected groups, the charge equations do not determine the charges uniquely, and the charge group associated to these D-branes is therefore in general not cyclic. The precise structure of the charge group depends on some number theoretic properties of n, d, and the level of the underlying affine algebra k. The examples of SO(3)=SU(2)/Z_2 and SU(3)/Z_3 are worked out in detail, and the charge groups for SU(n)/Z_d at most levels k are determined explicitly.Comment: 31 pages, 1 figure. 2 refs added. Added the observation: the charge group for each su(2) theory equals the centre of corresponding A-D-E grou

D-brane charges on SO(3)

In this letter we discuss charges of D-branes on the group manifold SO(3). Our discussion will be based on a conformal field theory analysis of boundary states in a Z_2-orbifold of SU(2). This orbifold differs from the one recently discussed by Gaberdiel and Gannon in its action on the fermions and leads to a drastically different charge group. We shall consider maximally symmetric branes as well as branes with less symmetry, and find perfect agreement with a recent computation of the corresponding K-theory groups.Comment: 11 pages, 1 figure. Some comments adde