We study the conditions to have supersymmetric D-branes on general N = 1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU (3) × SU (3) structure on T M ⊕ T ⋆ M , and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

We discuss the four-dimensional N = 1 effective approach in the study of warped type II flux compactifications with SU (3) × 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.

We study the dynamics governing space-time filling D-branes on Type II flux backgrounds preserving four-dimensional N = 1 supersymmetry. The four-dimensional superpotentials and D-terms are derived. The analysis is kept on completely general grounds thanks to the use of recently proposed generalized calibrations, which also allow one to show the direct link of the superpotentials and D-terms with BPS domain walls and cosmic strings respectively. In particular, our D-brane setting reproduces the tension of D-term strings found from purely four-dimensional analysis. The holomorphicity of the superpotentials is also studied and a moment map associated to the D-terms is proposed. Among different examples, we discuss an application to the study of D7-branes on SU (3)-structure backgrounds, which reproduces and generalizes some previous results.

The understanding of the fermionic sector of the worldvolume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory, like for example the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in absence of fluxes. A nonzero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.

We observe a direct relation between the existence of fundamental axionic strings, dubbed EFT strings, and infinite distance limits in 4d $$ \mathcal{N} $$ N = 1 EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as RG flow of their couplings, and allows one to probe different regimes within the field space of the theory. We propose that any 4d EFT infinite distance limit can be realised as an EFT string flow. We show that along such limits the EFT string becomes asymptotically tensionless, and so the EFT eventually breaks down. This provides an upper bound for the maximal field range of an EFT with a finite cut-off, and reproduces the Swampland Distance Conjecture from a bottom-up perspective. Even if there are typically other towers of particles becoming light, we propose that the mass of the leading tower scales as m2 ∼ $$ \mathcal{T} $$ T w in Planck units, with $$ \mathcal{T} $$ T the EFT string tension and w a positive integer. Our results hold even in the presence of a non-trivial potential, as long as its energy scale remains well below the cut-off. We check both proposals for large classes of 4d $$ \mathcal{N} $$ N = 1 string compactifications, finding that only the values w = 1, 2, 3 are realised.

Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle due to their large backreaction effects. In the context of 4d $$ \mathcal{N} $$ N = 1 EFTs, we consider $$ \frac{1}{2} $$ 1 2 BPS strings and membranes which are fundamental, in the sense that they cannot be resolved within the EFT regime. We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of these objects translates into a classical RG flow of their couplings. Constraints on the UV charges and tensions get then translated to constraints on the axionic kinetic terms and scalar potential of the EFT. This uncovers new relations among the Swampland Conjectures, which become interconnected by the physical properties of low-codimension objects. In particular, using that string RG flows describe infinite field distance limits, we show that the WGC for strings implies the Swampland Distance Conjecture. Similarly, WGC-saturating membranes generate a scalar potential satisfying the de Sitter Conjecture.

We find the effective action for any D-brane in a general bosonic background of supergravity. The results are explicit in component fields up to second order in the fermions and are obtained in a covariant manner. No interaction terms between fermions and the field f = b + F , characteristic of the bosonic actions, are considered. These are reserved for future work. In order to obtain the actions, we reduce directly from the M2-brane world-volume action to the D2-brane worldvolume action. Then, by means of T-duality, we obtain the other Dp-brane actions. The resulting Dp-brane actions can be written in a single compact and elegant expression.

We discuss a novel strategy to construct 4D N = 0 stable flux vacua of type II string theory, based on the existence of BPS bounds for probe D-branes in some of these backgrounds. In particular, we consider compactifications where D-branes filling the 4D space-time obey the same BPS bound as they would in an N = 1 compactification, while other D-branes, like those appearing as domain walls from the 4D perspective, can no longer be BPS. We construct a subfamily of such backgrounds giving rise to 4D N = 0 Minkowski no-scale vacua, generalizing the well-known case of type IIB on a warped Calabi-Yau. We provide several explicit examples of these constructions, and compute quantities of phenomenological interest like flux-induced soft terms on D-branes. Our results have a natural, simple description in the language of Generalized Complex Geometry, and in particular in terms of D-brane generalized calibrations. Finally, we extend the integrability theorems for 10D supersymmetric type II backgrounds to the N = 0 case and use the results to construct a new class of N = 0 AdS 4 compactifications. DWSB AdS4 vacua 61 11. Integrability of N = 0 vacua 63 11.1 Spinorial factorization of sourceless equations of motion 64 11.2 Adding calibrated sources 66 11.3 Integrability conditions for flux compactifications 69 11.4 Non-supersymmetric AdS 4 vacua from integrability 69 12. Conclusions and outlook 72 A. Supergravity conventions 75 A.1 Bosonic sector 75 A.2 Fermionic sector 76 A.3 Splitting to 4+6 dimensions and pure spinors 77 B. SUSY-breaking and pure spinors 79 B.1 Pure DWSB Minkowski backgrounds 81 C. The scalar curvature from pure spinors 82 D. Comments on non-geometric backgrounds 83 E. 10d integrability 84 F. Integrability of GKP vacua 87Indeed, from [6] we know that the supersymmetry conditions for a general flux background are equivalent to requiring that certain kinds of probe D-branes obey a BPS bound. 2 As we will show, this is only partially true in N = 0 GKP vacua, where a particular set of D-branes, namely some of those that look like domain-walls from the 4D viewpoint, no longer obey this BPS bound, and are thus intrinsically unstable in this background. On the other hand, D-branes that fill the 4D spacetime directions or look like strings in 4D still maintain their BPS properties unchanged with respect to the N = 1 case. This observation suggests an immediate way to generalize the GKP construction to other settings. Indeed, instead of considering the whole set of N = 0 supergravity compactifications to 4D Minkowski, we may restrict to those where 4D space-filling and string-like D-branes develop a BPS bound, while 4D domain walls will be lacking such a 'BPSness' property. The analysis of these backgrounds, which we dub 'Domain Wall SUSY-breaking' (DWSB) backgrounds, will be organized as follows:In Section 3 we translate the DWSB pattern in terms of the usual 10D gravitino and dilatino variations, in order to parameterize the space of DWSB backgrounds. Within this parameter space we single out a particular one-pa...