Related papers: Membranes and Sheaves
We compactify $M$-theory on a Calabi-Yau manifold to five dimensions by wrapping the membrane and fivebrane solitons of the eleven-dimensional supergravity limit around Calabi-Yau two-cycles and four-cycles respectively. We identify the…
We study rank $r$ cohomological Donaldson-Thomas theory on a toric Calabi-Yau orbifold of $\mathbb{C}^4$ by a finite abelian subgroup $\mathsf\Gamma$ of $\mathsf{SU}(4)$, from the perspective of instanton counting in cohomological gauge…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute. They contain an introduction to the subject and a…
Recently, Nekrasov discovered a new "genus" for Hilbert schemes of points on $\mathbb{C}^4$. We conjecture a DT/PT correspondence for Nekrasov genera for toric Calabi-Yau 4-folds. We verify our conjecture in several cases using a vertex…
The disk partition function of certain 3d N=2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d gauge theory/quantum K-theory correspondence for global and local Calabi-Yau manifolds…
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$…
This article provides a summary of arXiv:1701.08899 and arXiv:1701.08902 where the authors studied the enumerative geometry of nested Hilbert schemes of points and curves on algebraic surfaces and their connections to threefold theories,…
Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a…
Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.
Symmetric vacua of heterotic M-theory, characterized by vanishing cohomology classes of individual sources in the three-form Bianchi identity, are analyzed on smooth Calabi-Yau three-folds. We show that such vacua do not exist for…
We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…
In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA,…
Motivated by the six dimensional formulation of Kodaira-Spencer theory for Calabi-Yau threefolds, we formulate a two dimensional version and argue that this is the relevant field theory for the target space of local topological B-model with…
We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gauge theories on $\mathbb{R}^4$ and with two-dimensional…
We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7…
We study punctual quot-schemes of torsion-free sheaves $E_Y$ on smooth projective curves, surfaces and Calabi--Yau fourfolds via their virtual geometry. Our goal is to give a complete description of the virtual fundamental classes and their…
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…
We construct supergravity solutions dual to the twisted field theories arising when M-theory membranes wrap holomorphic curves in Calabi-Yau n-folds. The solutions are constructed in an Abelian truncation of maximal D=4 gauged supergravity…
A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our…