Related papers: K3 metrics
Quasi-BPS categories appear as summands in semiorthogonal decompositions of DT categories for Hilbert schemes of points in the three dimensional affine space and in the categorical Hall algebra of the two dimensional affine space. In this…
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We…
We show that BPS jumping loci -- loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner -- naturally appear as Fourier coefficients of (vector space-valued) automorphic…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well…
The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we…
We compute partition functions of the deformed multiple M5-branes theory on $K3\times T^2$ using the refined topological vertex formalism and the Borcherds lift. The deformation is related to the mass deformation in the corresponding four…
We study string theory propagating on R^6 times K3 by constructing orientifolds of Type IIB string theory compactified on the T^4/Z_N orbifold limits of the K3 surface. This generalises the Z_2 case studied previously. The orientifold…
Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kahler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex…
We use the gluing method to give a refined description of the collapsing Calabi-Yau metrics on Calabi-Yau 3-folds admitting a Lefschetz K3 fibration.
We study the cohomological properties of quasi-canonical lifts of an ordinary K3 surface over a finite field. As applications, we prove a Torelli type theorem for ordinary K3 surfaces over finite fields and establish the Hodge conjecture…
We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in $\mathbb{C}^2$ with cone singularities along a smooth complex curve. These metrics are expected to arise as blow up limits of non collapsed sequences of…
Following an overview of the relevant theory, we construct several explicit examples of height-3 K3 spectra.
In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product)…
The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find…
We consider deformations of N=1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds, characterised by non-zero vacuum expectation values for certain baryonic operators. Such baryonic…
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…
We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with…
We associate to the resolved conifold an affine special K\"{a}hler (ASK) manifold of complex dimension 1, and an instanton corrected hyperk\"{a}hler (HK) manifold of complex dimension 2. We describe these geometries explicitly, and show…
We propose an analytic method to calculate the matter field K\"ahler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field K\"ahler metric determines the normalisations…
We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R^{1,2}, the flat limit of…