New non-Kähler Calabi-Yau manifolds with balanced metrics and solutions to Strominger system.
problem Constructing compact non-Kähler Calabi-Yau manifolds.
method Proposed a new construction method and studied the Strominger system on these manifolds.
result Explicit solutions to the Strominger system with degeneracies on ΣgimesT4. Develops harmonic metrics for Hull-Strominger system stability.
problem Existence of solutions to the Hull-Strominger system with balanced class.
method Uses non-Hermitian Yang-Mills connections and holomorphic Courant algebroids, introduces harmonic metrics.
result Expected existence of a numerical stability condition for generic families of solutions.
Survey on Strominger system and Ricci flow in non-Kähler geometry.
problem Non-Kähler geometry on Calabi-Yau threefolds.
method Discussion of various geometric flows and equations.
result Exploration of balanced metrics and solutions to the Strominger system.
Solutions to Strominger system found for square of Kähler class.
problem Finding solutions to Strominger system with specific balanced classes.
method Deforming Calabi-Yau and Hermitian-Yang-Mills metrics.
result Classes that are squares of Kähler metrics admit solutions.
Lectures on Strominger system linking geometry, physics, and moduli.
problem Understanding Strominger system and its geometric and physical implications.
method Explains links with balanced metrics, Hermite-Yang-Mills, and generalized geometry.
result Illustrates Strominger system's role in moduli problems and generalized geometry.
Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.
problem Constructing representations of vertex algebras from non-Kähler solutions of the Hull-Strominger system.
method Embedding the N=2 superconformal vertex algebra in the chiral de Rham complex of a string Courant algebroid, with a condition on the Hermitian-Yang-Mills connection.
result Any solution of the Hull-Strominger system satisfying the Hermitian-Yang-Mills condition has an associated N=2 embedding.
Study shows existence of Strominger system solutions is not stable under complex structure deformations.
problem Stability of Strominger system solutions under complex structure deformations.
method Analyzes stability of solutions to the Strominger system in dimensions six, considering both positive and negative slope parameters.
result Existence of solutions to the Strominger system is neither open nor closed under holomorphic deformations of the complex structure.
Study of infinitesimal variations and moduli spaces in Strominger system and Killing spinors.
problem Understanding the moduli space of solutions to the Strominger system and related Killing spinor equations.
method Elliptic operator theory and generalized geometry to construct and describe the infinitesimal structure of the moduli space.
result Proposed a unifying framework for metrics with holonomy SU(3) and solutions of the Strominger system.
New solutions found for Hull-Strominger system on torus bundles.
problem Finding solutions to the Hull-Strominger system with torus symmetry.
method Constructing solutions on torus bundles over K3 orbifolds.
result Smooth manifolds with complex structures have solutions to the Hull-Strominger system.
Constructs solutions to Strominger system on Calabi-Yau 3-folds.
problem Solving the Strominger system on Calabi-Yau 3-folds.
method Noncompact Calabi-Yau 3-folds including C3 and resolved conifold O(−1,−1). result Constructs solutions to Strominger system on these spaces.
Paper finds infinitely many smooth solutions to complex geometry problem.
problem Finding smooth solutions to the Strominger system on specific geometric manifolds.
method Constructing solutions on generalized Calabi-Gray manifolds.
result Explicit construction of infinitely many solutions.
Study Hull-Strominger system and Anomaly flow on specific solvmanifolds.
problem Characterize invariant solutions to Hull-Strominger system and investigate flow of invariant metrics.
method Characterization of invariant solutions using Gauduchon connections, investigation of Anomaly flow, and proof of flow immortality under certain conditions.
result Anomaly flow reduces to a special form and always converges to a Kähler metric when slope parameter is zero.
New solutions found for complex structures on specific manifolds.
problem Constructing smooth solutions to the Hull-Strominger system.
method Using fibrations over K3 orbisurfaces.
result Proved existence of solutions for certain manifolds.
New geometric flow preserves balanced metrics and solves anomaly equations.
problem Balanced metrics and anomaly equations in Strominger systems.
method Introduced a geometric flow on (2,2)-forms preserving balanced metrics, using Nash-Moser implicit function theorem. result Existence of solutions for a short time established.
Researchers estimate a complex Hessian equation from Fu-Yau's generalization of a Strominger system.
problem Estimating a complex Hessian equation with gradients as right-hand side.
method Building on Fu and Yau's methods, obtaining a priori estimates in various smoothness classes.
result Identified difficulties in extending arguments for non-degeneracy from dimension 2 to higher dimensions.
New flow defined to solve Hull-Strominger system, with estimates and convergence results.
problem Constructing solutions to the Hull-Strominger system of equations.
method Introducing a natural extension of pluriclosed flow and using string algebroids and higher gauge theory.
result Proves global existence and convergence of the flow on special backgrounds.
New solutions found for complex geometry problem.
problem Solving the Hull-Strominger system on non-Kähler manifolds.
method Constructing solutions with a specific connection ansatz and using moduli spaces of sheaves.
result First T-dual solutions on compact non-Kähler manifolds with different topology.
New obstruction found for Hull-Strominger system solutions.
problem Existence of solutions to the Hull-Strominger system.
method Construction of Hermitian-Einstein metric on string algebroid.
result Definition of Futaki invariants obstructing solutions.
New solutions found for G2 system using K3 orbifolds.
problem Finding smooth solutions to the G2 Hull-Strominger system. method Torus fibrations over K3 orbifolds, adapted Serre construction for singular settings.
result Constructed new smooth solutions to the G2 Hull-Strominger system. Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on complex Lie groups. Both flat and non-flat cases are discussed in detail.
New T-dual solutions found for G2-Strominger system.
problem Compactification of heterotic string to three dimensions.
method Study of G2-structures with torsion coupled with G2-instantons. result Finite-dimensional moduli space of solutions and first T-dual examples. Given an irreducible unitary representation of a cocompact lattice of SL(2,C), we explicitly write down a solution of the Strominger system of equations. These solutions satisfy the equation of motion, and the underlying holomorphic vector bundles are stable.
Study on G2 structures and their moduli space in 7D.
problem Understanding moduli space of G2 structures with torsion. method Solving a system of partial differential equations related to the Bianchi identity.
result Moduli space of solutions is finite-dimensional.
Proves solutions to Fu-Yau equation on Kähler manifolds.
problem Existence of solutions to the Fu-Yau equation.
method Proof of existence on compact Kähler manifolds.
result Existence of non-trivial solutions to modified Strominger system.
New invariant solutions found for Strominger system and heterotic equations.
problem Invariant solutions to the Strominger system and heterotic equations of motion.
method Constructing solutions with a 2-parameter family of metric connections ablaε,ρ. result Explicit invariant solutions to the Strominger system with non-flat instanton and positive α′. Anomaly flow on Lie groups finds diverse behavior in solutions.
problem Finding solutions to the Hull-Strominger system on Lie groups.
method Examined the long-time behavior of the Anomaly flow on unimodular Lie groups.
result Diverse and intricate behavior of the Anomaly flow depends on Lie group and initial data.
Solves Fu-Yau equation for negative slope parameters in arbitrary dimensions.
problem Solving the Fu-Yau equation for negative slope parameters in arbitrary dimensions.
method Solves the Fu-Yau equation for negative slope parameters in arbitrary dimensions.
result First non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than 2.
New metrics solve complex equations on special 3D shapes.
problem Finding metrics on complex 3D shapes.
method Gluing construction to solve equations.
result Solves dilatino equation on small resolutions.
Paper constructs solutions to a system using Aeppli class without auxiliary gauge connection.
problem Constructing solutions to the Hull-Strominger system without auxiliary gauge connection.
method Deforming conformally balanced metric and tuning by Aeppli class to satisfy anomaly cancellation condition.
result Existence of family of solutions obtained via implicit function theorem.
String backgrounds yield simplified Hull-Strominger system solutions.
problem Solving the simplified Hull-Strominger system in various geometries.
method Variational argument using string action, gradient Ricci solitons, and symmetry reduction.
result Canonical symmetry and transverse geometry properties derived.
We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the eq…
Study proves Kählerness criteria for Hermitian surfaces under specific curvature conditions.
problem Determining when Hermitian surfaces are Kählener.
method Used explicit identities linking Strominger-Bismut Ricci curvatures to torsion, and Chern number identities.
result Proves several Kählerness criteria for compact Hermitian surfaces.
Proves Strominger connection's Kähler-like condition implies pluriclosed metric.
problem Understanding Strominger connection's implications for Hermitian manifolds.
method Analyzes curvature symmetries and torsion properties.
result Strominger Kähler-like condition is equivalent to pluriclosed metric plus parallel torsion.
The Strominger conjecture is confirmed for compact Hermitian manifolds in 2D and special higher dimensions.
problem Determining conditions for a Hermitian metric to be Kähler based on the Strominger connection's curvature.
method Analyzing the Strominger connection's holomorphic sectional curvature in compact Hermitian manifolds.
result The Strominger conjecture is confirmed in 2D and special higher dimensions.
The paper studies the local structure of a moduli space for a specific string theory system.
problem Investigating the local structure of the moduli space of solutions to the Hull--Strominger system.
method Using a vector bundle and studying the deformation complex associated with a differential operator $ar{D}$, establishing an isomorphism between cohomology groups.
result The moduli space has an expected dimension of zero.
New Ricci flow solutions found via T-duality.
problem Finding new solutions to Ricci flow equations.
method Introducing Ricci flow in generalized geometry and using T-duality.
result Solutions of Ricci flow and Killing spinor equations are exchanged under T-duality.
The study characterizes Hermitian manifolds with parallel Bismut-Strominger torsion.
problem Characterizing Hermitian manifolds with specific torsion properties.
method Analyzing the curvature tensor and properties of the Bismut-Strominger connection.
result A necessary and sufficient condition for Bismut torsion parallel manifolds.
This work extends Yau's theorem to non-Kähler manifolds using holomorphic Courant algebroids.
problem Extending Yau's theorem to non-Kähler manifolds.
method Defining equations based on a mild generalization of the Hull-Strominger system and using Bott-Chern secondary characteristic classes.
result Existence of canonical metrics on holomorphic Courant algebroids.
Anomaly flow studied on flat and non-flat nilmanifolds.
problem Analyzing the Anomaly flow on nilmanifolds.
method Examined with respect to Hermitian connections, focusing on flat and non-flat cases.
result General solutions and qualitative behavior of the Anomaly flow on nilmanifolds.
New equivalence found between Yang-Mills and heterotic G2 structures.
problem Understanding instanton connections and moduli spaces in string theory.
method Rephrasing heterotic G2 systems in terms of differential operators and instanton conditions.
result Strominger-Hull system equivalent to holomorphic Yang-Mills on restricted manifolds.
This article surveys the development of the SYZ conjecture since it was proposed by Strominger, Yau and Zaslow in their famous 1996 paper, and discusses how it has been leading us to a thorough understanding of the geometry underlying mirror symmetry.
The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian then any invariant balanced J-…
New insights on ACYT 6-manifolds reveal instanton conditions for curvature.
problem Understanding instanton conditions on ACYT 6-manifolds.
method Analyzing curvature and torsion properties of ACYT 6-manifolds.
result Curvature is an SU(3)-instanton if and only if torsion is parallel. Conformally compact and complete smooth solutions to the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton using the first Pontrjagin form of the (-)-connection} on 6-dimensional non-Kaehler nilmanifold are presented. In the conformally compact case the dilaton is determined by t…
The article confirms a complex geometry conjecture for a specific type of manifold.
problem Compact Hermitian manifolds with constant holomorphic sectional curvature.
method Restricting to pluriclosed manifolds and confirming the conjecture for Strominger Kähler-like manifolds.
result The conjecture is confirmed for a specific type of Hermitian manifold.
Study Gauduchon connections on Kähler-like metrics in 6D solvmanifolds.
problem Investigate Hermitian metrics with Gauduchon connections having symmetries similar to Levi-Civita and Chern connections.
method Analyze 6-dimensional solvmanifolds with invariant complex structures and trivial canonical bundles. result Evidence supports two conjectures about Kähler-like conditions for different Gauduchon connections.
Classifies 6D homogeneous spaces with holomorphically trivial canonical bundle.
problem Classifying 6D homogeneous spaces with specific geometric properties.
method Analyzing Lie algebras and homogeneous spaces, studying connections and instantons.
result Compact non-Kähler homogeneous spaces are unique in their solutions to the Hull-Strominger system.
Introduces gauge theory for string algebroids, solving Calabi system.
problem Solving coupled equations for Calabi problem and Hull-Strominger system.
method Moment map picture with Hamiltonian gauge action, inner automorphisms of Courant algebroids.
result Moduli space carries pseudo-Kähler metric with Kähler potential given by dilaton functional.