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Register a new userHints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
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We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the integrability and flatness conditions. The B model geometry defines an interesting ring structure of operators. For the mirror A model this indicates the existence of an open-string extension of the so-called A model connection, whereas the discovered ring structure should be part of the open-string A model quantum cohomology. We obtain predictions for genuine Ooguri-Vafa invariants for Lagrangian branes on the quintic in P4 that pass some non-trivial consistency checks. We discuss the lift of the brane compactifications to F-theory on Calabi-Yau 4-folds and the effective couplings in the effective supergravity action as determined by the N = 1 special geometry of the open-closed deformation space.
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We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the off-shell superpotential and its analytic properties under deformation. Explicit expressions for the N=1 superpotential for families of type II/F-theory compactifications are obtained for a list of multi-parameter examples. Using the Hodge theoretic approach to open-string mirror symmetry, we obtain new predictions for integral disc invariants in the A model instanton expansion. We study the behavior of the brane vacua under extremal transitions between different Calabi-Yau spaces and observe that the web of Calabi-Yau vacua remains connected for a particular class of branes.
We summarize the foliation approach to ${cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $mathrm{AdS}_3$ spaces for the case when the internal part $xi$ of the supersymmetry generator is chiral on some proper subset ${cal W}$ of $M$. In this case, a topological no-go theorem implies that the complement $Msetminus {cal W}$ must be a dense open subset, while $M$ admits a singular foliation ${bar {cal F}}$ (in the sense of Haefliger) which is defined by a closed one-form $boldsymbol{omega}$ and is endowed with a longitudinal $G_2$ structure. The geometry of this foliation is determined by the supersymmetry conditions. We also describe the topology of ${bar {cal F}}$ in the case when $boldsymbol{omega}$ is a Morse form.
We study the physics of F-theory compactifications on genus-one fibrations without section by using an M-theory dual description. The five-dimensional action obtained by considering M-theory on a Calabi-Yau threefold is compared with a six-dimensional F-theory effective action reduced on an additional circle. We propose that the six-dimensional effective action of these setups admits geometrically massive U(1) vectors with a charged hypermultiplet spectrum. The absence of a section induces NS-NS and R-R three-form fluxes in F-theory that are non-trivially supported along the circle and induce a shift-gauging of certain axions with respect to the Kaluza-Klein vector. In the five-dimensional effective theory the Kaluza-Klein vector and the massive U(1)s combine into a linear combination that is massless. This U(1) is identified with the massless U(1) corresponding to the multi-section of the Calabi-Yau threefold in M-theory. We confirm this interpretation by computing the one-loop Chern-Simons terms for the massless vectors of the five-dimensional setup by integrating out all massive states. A closed formula is found that accounts for the hypermultiplets charged under the massive U(1)s.
The properties of the effective scalar potential are studied in the framework of type IIB string theory, taking into account perturbative and non-perturbative corrections. The former modify the Kahler potential and include $alpha$ and logarithmic corrections generated when intersecting D7 branes are part of the internal geometric configuration. The latter add exponentially suppressed Kahler moduli dependent terms to the fluxed superpotential. The possibility of partial elimination of such terms which may happen for particular choices of world fluxes is also taken into account. That being the case, a simple set up of three Kahler moduli is considered in the large volume regime, where only one of them is assumed to induce non-perturbative corrections. It is found that the shape of the F-term potential crucially depends on the parametric space associated with the perturbative sector and the volume modulus. De Sitter vacua can be obtained by implementing one of the standard mechanisms, i.e., either relying on D-terms related to $U(1)$ symmetries associated with the $D7$ branes, or introducing $overline{D3}$ branes. In general it is observed that the combined effects of non-perturbative dynamics and the recently introduced logarithmic corrections lead to an effective scalar potential displaying interesting cosmological and phenomenological properties.
We present an unfolded off-shell formulation for free massless higher-spin fields in 4d Minkowski space in terms of spinorial variables. This system arises from the on-shell one by the addition of external higher-spin currents, for which we find an unfolded description. Also we show that this off-shell system can be interpreted as Schwinger-Dyson equations and restore two-point functions of higher-spin fields this way.
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