arXiv research

The cohomology ring of certain Lagrangian 3-manifolds is analyzed, influencing quantum Reidemeister torsion and superpotential.

New groups and manifolds from Weyl groups, with Frobenius structures.

Study of B-type LG models on open Riemann surfaces.

The study extends Frobenius manifold structures for root systems of type B, C, and D.

The paper proves mirror symmetry for del Pezzo surfaces and computes related structures.

We consider Landau-Ginzburg (LG) models with boundary conditions preserving A-type N=2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the corresponding CFT by an explicit computation of the open-string Witten index in the LG mo…

We classify superpotentials for cohomogeneity one Ricci solitons, finding new ones and proving non-existence in higher dimensions.

Geometrically computes superpotentials for certain 4D N=2 theories.

Study finite deformations from heterotic superpotential, leading to new complex effective action.

The paper extends a proposal for effective twisted superpotentials to higher rank.

We extend our previous classification of superpotentials of ``scalar curvature type" for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in our previous paper, i.e., when some weight vector of the superpotential lies outside (a scaled translate of) the convex hull of the weight vectors …

Study Hodge theory for Landau-Ginzburg models on Calabi-Yau manifolds.

A model for B-type Landau-Ginzburg theories rigorously defined.

Study compares thimbles to Morse theory on Lie theory models.

This study compares Landau-Ginzburg theory to Khovanov homology.

Establishes correspondence between Calabi-Yau and Landau-Ginzburg structures.

New models for B-type topological theories using complex functions.

We give an overview of our earlier classification results in [DW4] and [DW6] for superpotentials of scalar curvature type of the cohomogeneity one Ricci-flat equations. We then give an account of the classification in the case where the isotropy representation of the principal orbit consists of exactly three distinct i…

Generalizes Landau-Ginzburg mirrors for Frobenius manifolds in Dynkin type A.

Study simplifies Landau-Ginzburg models on Stein manifolds.

The paper proves an isomorphism between $tt^*$ structures of Landau-Ginzburg and Calabi-Yau models.

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…

Study cohomologies of complex bundles and sections.

Infinitely many M2-instantons affect M-theory on G2-manifolds.

Study connects mirror symmetry invariants to K-stability for toric manifolds.

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tenso…

We study N=2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kahler or bihermitian target space manifolds. We determine the most general local N=2 superconformal boundary conditions (D-branes) for these sigma mod…

Maps Kähler cones to moduli spaces of stable manifolds.

The paper constructs monopole Floer homology for specific 3-manifolds and surfaces.

New insights into mirror symmetry via Monge-Ampère domains and pre-Frobenius manifolds.

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…

The study connects K-stability and large complex structure limits in mirror symmetry.

Explains complex adjoint orbits in Lie theory and geometry.

Paper constructs solutions to WDVV equations for Frobenius manifolds.

The abstract proves a conjecture about geometric structures in Calabi-Yau orbifolds.

Novel $A_{\infty}$-categories derived from gauge theories for manifold homologies.

We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of Kähler type in five dimensions.

New construction of Fukaya-Seidel categories using complex gradient flow equation.

Geometrically constructs energy-tensors for gauge and gravitational fields.

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence …

We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the Landau-Ginburg orbifold. As an application, we prove an explicit orbifold formula for the elliptic genus of Calabi-Yau hypersurfa…

We study the four-dimensional effective theory arising from ten-dimensional heterotic supergravity compactified on manifolds with torsion. In particular, given the heterotic superpotential appropriately corrected at $\mathcal{O}(α')$ to account for the Green-Schwarz anomaly cancellation mechanism, we investigate proper…

Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X. This establishes part of the Homological Mirror Conjecture for toric var…

We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity. On a d-dimensional background, as first described by Hull, the action of the generalised geometrical O(d…

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The $SU(2)_{local}\times SU(2)_{global}$ N=4 superconformal symmetry of the particle action requires the background to be a real "Kähler-like" manifold whose metric is generated by a sigma-model superpotenti…

To construct mirror symmetric Landau-Ginzburg models, P.Berglund, T.Hübsch and M.Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of its symmetries together with a dual pair $(\widetilde{f}, \widetilde{G})$. Here we study the reduced orbifold Euler characteristics…

We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations, or equations for harmonic maps into SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and (iii) monodromy data. This allows us to find all solutions with integral Stokes data. These include solu…

Study special complexified Kähler forms in mirror symmetry.