Related papers: Wall-crossing of D4-branes using flow trees
We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…
We consider the refined $\mathrm{SU}(r)$ Vafa-Witten partition function of a smooth projective surface with non-zero holomorphic 2-form. This partition function has a vertical contribution, expressible in terms of nested Hilbert schemes.…
We show that the topological string partition function with D-branes on a compact Calabi-Yau manifold has new anomalies that spoil the recursive structure of the holomorphic anomaly equation and introduce dependence on wrong moduli (such as…
An important subclass of D-branes on a Calabi-Yau manifold, X, are in 1-1 correspondence with objects in D(X), the derived category of coherent sheaves on X. We study the action of the monodromies in Kaehler moduli space on these D-branes.…
Supersymmetric D-branes supported on the complex two-dimensional base $S$ of the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent sheaves on $S$. Under suitable conditions, the BPS indices counting these objects (known…
We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…
We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone,…
Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we…
We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes. The presence of D6-brane deformation moduli redefines the 4d dilaton and complex structure fields and complicates the analysis of such vacua in terms of the…
We study the 'Large Volume Scenario' on explicit, new, compact, four-modulus Calabi-Yau manifolds. We pay special attention to the chirality problem pointed out by Blumenhagen, Moster and Plauschinn. Namely, we thoroughly analyze the…
Following an eight-dimensional gauged supergravity approach we construct the most general solution describing D6-branes wrapped on a Kahler four-cycle taken to be the product of two spheres of different radii. Our solution interpolates…
We analyze the link between the occurrence of massless B-type D-branes for specific values of moduli and monodromy around such points in the moduli space. This allows us to propose a classification of all massless B-type D-branes at any…
We study the D3-brane moduli dependence of the non-perturbative superpotential generated by the D7-brane gaugino condensation in a type IIB compactification on an orientifold of the elliptic Calabi-Yau threefold $\Bbb{P}_{[1,1,1,6,9]}[18].$…
The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of…
Generating functions $h_r(\tau)$ of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a…
We explicitly construct and study the statistics of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau hypersurface $P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. We solve for these moduli…
We construct a statistical model that correctly reproduces the BPS partition function of D4-D2-D0 bound states on the resolved conifold. We prove that the known partition function of the BPS indices is reproduced by the counting "triangular…
The N=1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from a Kaluza-Klein reduction. The Kahler potential, the gauge kinetic functions and the flux-induced superpotential are…
In this paper we compute the N=1 effective low energy action for a stack of N space-time filling D3-branes in generic type IIB Calabi-Yau orientifolds with non-trivial background fluxes by reducing the Dirac-Born-Infeld and Chern-Simons…
This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry. We introduce the notion of…