On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds

We derive the complete supergravity description of the N=2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)}, obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric superpotential W$ proposed, some time ago, by Berglund and Mayr.Comment: 14 pages, LaTeX sourc

N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.Comment: 24 pages; v2: reference adde

Canonical differential geometry of string backgrounds

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes.Comment: 20 pages, no figures, improved journal versio

Conifolds and Geometric Transitions

Conifold geometries have recieved a lot of attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the "warped throat". It is our intention in this article to give a pedagogical explanation for the singularity resolution in this geometry and emphasise its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, which we also explain from a T-dual intersecting branes scenario. We then make the connection to the Gopakumar-Vafa conjecture for open/closed string duality and summarise a series of papers verifying this model on the supergravity level. An appendix provides extensive background material about conifold geometries. We pay special attention to their complex structures and re-evaluate the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds. We agree with earlier results that only the singular solution allows a supersymmetric flux, but point out the importance of using the correct complex structure to reach this conclusion.Comment: 37 pages, v3: accepted for publication in Reviews of Modern Physic

Passenger car equivalent for heavy vehicles crossing turbo-roundabouts

Turbo-roundabouts represent an innovative scheme of modern roundabouts which provides a spiraling traffic flow and requires drivers to choose their direction before entering the intersection, since raised lane separators mark the lanes on the ring. The configuration of the turbo-roundabout makes that patterns of conflict at entries with one and two conflicting traffic streams can coexist. This paper presents research efforts aimed at measuring quantitatively the effect of heavy vehicles on operational conditions of a turbo-roundabout. The study starts from the initial belief that the greatest constraints to the vehicular trajectories imposed by the turbo-roundabout necessarily imply that the impact of heavy vehicles on the quality of traffic flow is more unfavorable than on other modern roundabouts. Microsimulation revealed as a useful tool when the variation of the traffic quality in turbo-roundabouts should be evaluated in presence of mixed fleets, each having different percentages of heavy vehicles; indeed, it allowed to isolate traffic conditions difficult to observe on field and replicate them to have a number of data as much as possible numerous. Entry capacity values for each entry lane of the turbo-roundabout were obtained by microsimulation, varying the percentage of heavy vehicles for entering flows. Nonlinear regression analysis of simulation data allowed to derive the behavioral parameters for heterogeneous populations of users and, ultimately, composed exclusively of heavy vehicles. The capacity functions thus obtained allowed us to determine how the passenger car equivalent (PCE) varies with the percentage of heavy vehicles and circulating flows for each entry lane of the turbo-roundabout. The results of this study indicate that there is a need to distinguish the impact of heavy vehicles when analyzing the capacity of a turbo-roundabout. When the traffic stream contains a significant number of heavy vehicles, a larger PCE effect would be expected. This effect should be accounted for in the estimation of the turbo-roundabout capacity. Lastly it should be emphasized that an important aspect of the research consists in having identified a methodology for assessing the impact of heavy vehicles on the quality of traffic flow, that can be applied to different patterns of intersection

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

Gravity duals to deformed SYM theories and Generalized Complex Geometry

We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of N =4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.Comment: LaTex, 29 page

Supersymmetric AdS(4) compactifications of IIA supergravity

We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.Comment: 24 pages, references adde

Towards Minkowski Vacua in Type II String Compactifications

We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3)xSU(3) structure. We argue that generalised geometry enables us to treat these non-geometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values.Comment: 33 pages; v2 minor corrections, references added, version to appear in JHE