Related papers: Instantons and branes in manifolds with vector cro…
The effective four-dimensional supergravity of M-theory compactified on the orbifold S^1/Z_2 and a Calabi-Yau threefold includes in general moduli supermultiplets describing massless modes of five-branes. For each brane, one of these fields…
We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are…
We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds are investigated.
In a toroidal orbifold of type IIB string theory we study instanton effects in N=2 super Yang-Mills theories engineered with systems of wrapped magnetized D9 branes and Euclidean D5 branes. We analyze the various open string sectors in this…
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 study the Gepner model description of D-branes in Calabi-Yau manifolds with singular curves. From a geometrical point of view, the resolution of singularities leads to additional homology cycles around which branes can wrap. Using…
As a first step towards studying vector bundle moduli in realistic heterotic compactifications, we identify all holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. Computing the homology, we find that…
We analyze the phase structure of topological Calabi--Yau manifolds defined on the moduli space of instantons. We show in this framework that topological vacua describe new phases of the Heterotic String theory in which the flat directions…
We extend the study of superinstantons presented in 1905.01513 to include orthosymplectic supergroup gauge theories, $B_{n_0|n_1}$, $C_n$, and $D_{n_0|n_1}$. We utilize equivariant localization to obtain the LMNS contour integral formula…
We review a method to construct $\rm{G}_2$--instantons over compact $\rm{G}_2$--manifolds arising as the twisted connected sum of a matching pair of Calabi-Yau $3$-folds with cylindrical end, based on the series of articles [SE15, SEW15,…
We study the collision of two flat, parallel end-of-the-world branes in heterotic M-theory. By insisting that there is no divergence in the Riemann curvature as the collision approaches, we are able to single out a unique solution…
We consider a class of special Lagrangian subspaces of Calabi-Yau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of…
This is the first nontrivial construction to date of instantons over a compact manifold with holonomy exactly $G_2$. The HYM connections on asymptotically stable bundles over Kovalev's noncompact Calabi-Yau 3-folds, obtained in the first…
By blowing up the ambient space along the curve wrapped by B-branes, we study the brane superpotentials and Ooguri-Vafa invariants on complete intersections Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials are…
We argue that D-branes corresponding to rational B boundary states in a Gepner model can be understood as fractional branes in the Landau-Ginzburg orbifold phase of the linear sigma model description. Combining this idea with the…
There have been a number of constructions of Lagrangian Floer homology invariants for $3$-manifolds defined in terms of symplectic character varieties arising from Heegaard splittings. With the aim of establishing an Atiyah-Floer…
We introduce the concept of a branched holomorphic Cartan geometry. It generalizes to higher dimension the definition of branched (flat) complex projective structure on a Riemann surface introduced by Mandelbaum. This new framework is much…
Quantum non-perturbative geometry of the universal hypermultiplet is investigated. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the universal…
We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau threefold compactifications of type IIA strings. These corrections are mirror to the D1…
We show that Calabi-Yau crystals generate certain Chern-Simons knot invariants, with Lagrangian brane insertions generating the unknot and Hopf link invariants. Further, we make the connection of the crystal brane amplitudes to the…