The non-abelian D-brane effective action through order α′4\alpha'{}^4

Requiring the existence of certain BPS solutions to the equations of motion, we determine the bosonic part of the non-abelian D-brane effective action through order $\alpha'{}^4$. We also propose an economic organizational principle for the effective action.Comment: 12 pages, 2 figures, JHEP styl

Generalized geometry, calibrations and supersymmetry in diverse dimensions

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl

A landscape of non-supersymmetric AdS vacua on coset manifolds

We construct new families of non-supersymmetric sourceless type IIA AdS4 vacua on those coset manifolds that also admit supersymmetric solutions. We investigate the spectrum of left-invariant modes and find that most, but not all, of the vacua are stable under these fluctuations. Generically, there are also no massless moduli.Comment: 20 pages, 11 figures, v2: added some clarifications, references, v3: corrections addressing comments refere

Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace

We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the calculation. Performing the calculation through three loops yields the equations of motion up to five derivatives on the fieldstrengths, which upon integration gives the bosonic sector of the effective action for a single D-brane in trivial bulk background fields through four derivatives and to all orders in alpha'. Finally, the present calculation shows that demanding ultra-violet finiteness of the non-linear sigma-model can be reformulated as the requirement that the background is a deformed stable holomorphic U(1) bundle.Comment: 25 pages, numerous figure

Reformulating Supersymmetry with a Generalized Dolbeault Operator

The conditions for N=1 supersymmetry in type II supergravity have been previously reformulated in terms of generalized complex geometry. We improve that reformulation so as to completely eliminate the remaining explicit dependence on the metric. Doing so involves a natural generalization of the Dolbeault operator. As an application, we present some general arguments about supersymmetric moduli. In particular, a subset of them are then classified by a certain cohomology. We also argue that the Dolbeault reformulation should make it easier to find existence theorems for the N=1 equations.Comment: 30 pages, no figures. v2: minor correction

D-branes on AdS flux compactifications

We study D-branes in N=1 flux compactifications to AdS_4. We derive their supersymmetry conditions and express them in terms of background generalized calibrations. Basically because AdS has a boundary, the analysis of stability is more subtle and qualitatively different from the usual case of Minkowski compactifications. For instance, stable D-branes filling AdS_4 may wrap trivial internal cycles. Our analysis gives a geometric realization of the four-dimensional field theory approach of Freedman and collaborators. Furthermore, the one-to-one correspondence between the supersymmetry conditions of the background and the existence of generalized calibrations for D-branes is clarified and extended to any supersymmetric flux background that admits a time-like Killing vector and for which all fields are time-independent with respect to the associated time. As explicit examples, we discuss supersymmetric D-branes on IIA nearly Kaehler AdS_4 flux compactifications.Comment: 43 pages, 2 pictures, 1 table; v2: added references, color to figure and corrected typo in (6.21b

From ten to four and back again: how to generalize the geometry

We discuss the four-dimensional N=1 effective approach in the study of warped type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N=1 flux vacua in full generality. We find that the non-perturbative corrections induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications 'destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.Comment: LaTeX, 47 pages, v2, references, hyperref added, v3, correcting small inaccuracies in eqs. (2.6a) and (5.16

The problematic backreaction of SUSY-breaking branes

In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.Comment: 27 pages, Latex2e, 5 figure

AdS4 flux vacua in type II superstrings and their domain-wall solutions

We investigate the emergence of supersymmetric negative-vacuum-energy ground states in four dimensions. First, we rely on the analysis of the effective superpotential, which depends on the background fluxes of the internal manifold, or equivalently has its origin in the underlying gauged supergravity. Four-dimensional, supersymmetric anti-de Sitter vacua with all moduli stabilized appear when appropriate Ramond and Neveu--Schwarz fluxes are introduced in IIA. Geometric fluxes are not necessary. Then the whole setup is analyzed from the perspective of the sources, namely D/NS-branes or Kaluza--Klein monopoles. Orientifold planes are also required for tadpole cancellation. The solutions found in four dimensions correspond to domain walls interpolating between AdS4 and flat spacetime. The various consistency conditions (equations of motion, Bianchi identities and tadpole cancellation conditions) are always satisfied, albeit with source terms. We also speculate on the possibility of assigning (formal) entropies to AdS4 flux vacua via the corresponding dual brane systems.Comment: Acknowledgment replace

Higher order contributions to the effective action of N=2 super Yang-Mills

We apply heat kernel techniques in N=1 superspace to compute the one-loop effective action to order $F^5$ for chiral superfields coupled to a non-Abelian super Yang-Mills background. The results, when combined with those of hep-th/0210146, yield the one-loop effective action to order $F^5$ for any N=2 super Yang-Mills theory coupled to matter hypermultiplets.Comment: 23 pages, references adde