Factorization properties of genus-two bosonic and fermionic string partition functions

The genus-two bosonic and fermionic string partition functions factorize, in the separating pinching limit, into genus-one partition functions after integrating out the supermoduli with super-Beltrami support on the puncture points in the fermionic and heterotic case

Flux compactification on smooth, compact three-dimensional toric varieties

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques which allow us to systematically construct G-structures on SCTV and read off their torsion classes. We illustrate our methods with explicit examples, one of which consists of an infinite class of toric CP^1 bundles. We give a self-contained review of the relevant concepts from toric geometry, in particular the subject of the classification of SCTV in dimensions less or equal to 3. Our results open up the possibility for a systematic construction and study of supersymmetric flux vacua based on SCTV.Comment: 27 pages, 10 figures; v2: references, minor typos & improvement

New supersymmetric AdS4 type II vacua

Building on our recent results on dynamic SU(3)xSU(3) structures we present a set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type IIA/IIB supergravity. These conditions ensure that the background solves, besides the supersymmetry equations, all the equations of motion of type II supergravity. The conditions state that the internal manifold is locally a codimension-one foliation such that the five dimensional leaves admit a Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total six-dimensional internal space is locally an S^2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. Given any five-dimensional Sasaki-Einstein manifold we construct the corresponding families of type IIA/IIB vacua. The precise profiles of all the fields are determined at the solution and depend on whether one is in IIA or in IIB. In particular the background does not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant.Comment: 19 pages; clarifications added, version to appear in JHE

N=1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes

We consider N=1 compactifications of the type-IIA theory on the T6/(Z2xZ2) orbifold and O6 orientifold, in the presence of D6-branes and general NSNS, RR and Scherk-Schwarz geometrical fluxes. Introducing a suitable dual formulation of the theory, we derive and solve the Bianchi identities, and show how certain combinations of fluxes can relax the constraints on D6-brane configurations coming from the cancellation of RR tadpoles. We then compute, via generalized dimensional reduction, the N=1, D=4 effective potential for the seven main moduli, and comment on the relation with truncated N=4 gaugings. As a byproduct, we obtain a general geometrical expression for the superpotential. We finally identify a family of fluxes, compatible with all Bianchi identities, that perturbatively stabilize all seven moduli in supersymmetric AdS4.Comment: 19 pages, no figures, JHEP3 LaTeX. Published versio

Four-dimensional heterotic strings-orbifolds and covariant lattices

Two - so far unrelated - constructions of four-dimensional heterotic string theories are discussed within a common framework. We show that four-dimensional heterotic string theories which are based on covariant self-dual lattices are equivalent to a wide class of asymmetric orbifolds. This equivalence provides an explicit realization of twist fields and allows the straight-forward calculation of scattering amplitudes of various massless fields. “Topological” properties of the orbifolds, like the number of fixed points, are related to group theoretical features of the covariant lattices. Two explicit examples illustrate our conclusions

Moduli Stabilization in Type IIB Orientifolds (I)

We discuss flux quantization and moduli stabilization in toroidal type IIB Z_N - or Z_N x Z_M -orientifolds, focusing mainly on their orbifold limits. After presenting a detailed discussion of their moduli spaces and effective actions, we study the supersymmetric vacuum structure of these models and derive criteria for the existence of stable minima. Furthermore, we briefly investigate the models away from their orbifold points and comment on the microscopic origin of their non-perturbative superpotentials.Comment: 97 pages + 2 figs, harvma

On supersymmetric Minkowski vacua in IIB orientifolds

Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such vacua. By taking additional gaugino condensation on fixed space-time filling D3-branes into account also models without complex structure can be consistently stabilized to Minkowski vacua.Comment: 17 pages, 2 figures; More detailed proof for absence of complex flat directions in susy AdS vacua given; Footnotes and reference adde

D3 Brane Action and Fermion Zero Modes in Presence of Background Flux

We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an Euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T^6/Z_2, six of the sixteen zero modes originally present are lifted by the flux.Comment: Important factor of ``i'' was overlooked in Euclidean continuation of WZ term. This changes the count of zero-modes in the T^6/Z_2 example. Main result stays unchanged. We thank Bergshoeff, Kallosh, Kashani-Poor, Sorokin and Tomasiello for pointing this ou

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

From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.Comment: LaTeX, 37 pages. Some typos fixed. Final version, to appear in Nucl. Phys.