Generalized non-supersymmetric flux vacua

Abstract

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...

On D-brane moduli stabilisation

“…(2.8) to be satisfied. Such component will raise the energy of the compactification via the 4d effective potential computed in [34] …”

On the stability of non-supersymmetric AdS vacua

“…In the D4-brane case the lower bound follows from the fact that the Kahler form on the Calabi-Yau is a calibration 17 . For the sake of clarity let us pause to quickly review how this comes about.…”

“…Early papers on IIA compactifications include [10] which developed the 4D framework, and [11], [12], which discuss Moduli stabilization. Also see, [13], [14], [17], [18], [19]. A recent discussion on non-perturbative decays, especially decays of Minkowski nearly susy vacua to AdS space and related topics, is in [15].…”

DWSB in heterotic flux compactifications

“…This latter observation was used in [15] to propose a general strategy for constructing N = 0 vacua in the context of type II flux compactifications. In this approach one assumes that the ten-dimensional background allows for a globally defined spinor which, from the four-dimensional viewpoint will be the generator of an approximate supersymmetry.…”