A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Introduces holomorphic string algebroids and classifies them.
Introduces gauge theory for string algebroids, solving Calabi system.
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of -gerbes. At the same time, transitive Courant algebroids may be viewed as the higher analogue of Atiyah Lie algebroids, and the non-commutative a…
In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby determine global conditions for the existence of T-duals in heterotic string theory. In particular we find that T-duality exch…
Holomorphic Lie algebroid connections on Riemann surfaces are characterized.
Develops Palatini formalism in generalized geometry for string theory.
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A …
Study families of Lie algebroids on complex spaces, introducing unfoldings.
Develops theory of para-holomorphic algebroids with para-complex connections.
Reformulates compatibility condition for generalized metrics in string theory.
Y-algebroids generalize symmetry structures for string/M-theory compactifications.
Criterion for Lie algebroid connections on compact Riemann surfaces.
Defines connections on parabolic vector bundles for Lie algebroids.
Defines and examines morphisms of Courant algebroids with applications in physics.
Study connections on complex Riemann surfaces for Lie algebroid structures.
We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions. We then apply this to obta…
Extends Lie bialgebroids for string and M theories with new calculus framework.
Develops theory of para-holomorphic algebroids on Calabi-Yau manifolds.
We study the semidirect product of a Lie algebra with a representation up to homotopy and provide various examples coming from Courant algebroids, string Lie 2-algebras, and omni-Lie algebroids. In the end, we study the semidirect product of a Lie group with a representation up to homotopy and use it to give an integra…
Complex Finsler vector bundles have been studied mainly by T. Aikou, who defined complex Finsler structures on holomorphic vector bundles. In this paper, we consider the more general case of a holomorphic Lie algebroid E and we introduce Finsler structures, partial and Chern-Finsler connections on it. First, we recall …
New geometries defined for string models, filling gaps in the literature.
We prove that a holomorphic Lie algebroid is integrable if, and only if, its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic-Fernandes do also apply in the holomorphic context without any modification. As a consequence we give another proof of the following theorem: a holomorphic…
Study of Hermitian metrics on Lie algebroids over complex spaces.
Defines T-duality and generalised Ricci flow relations using Courant algebroid relations.
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a compl…
Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connect…
Paper develops a unified framework for Lie algebroid connections on various bundles.
Study of exceptional algebroids in type IIA string theory.
Study Lie algebroid connections on principal bundles over complex projective varieties.
New algebroids allow studying various geometries simultaneously.
We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We consider the matched sum of two Dirac subbundles, one in each of two Courant algebroids forming a matched pair.
We introduce the notion of Glanon groupoids, which are Lie groupoids equipped with multiplicative generalized complex structures. It combines symplectic groupoids, holomorphic Lie groupoids and holomorphic Poisson groupoids into a unified framework. Their infinitesimal, Glanon Lie algebroids are studied. We prove that …
The paper explores linear generalised complex structures over vector bundles.
Criterion found for Lie algebroid connections on parabolic bundles.
Established equivalence of Atiyah classes for generalized holomorphic vector bundles.
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All of the Laplace opera…
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special Kähler geometry and the ring of almost-holomorphic modular forms defined on modular curves.
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are …
It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex structures. On general grounds such D-branes (called generalized complex (GC) branes) must form a category. We compute the BRST cohomology of open strings …
Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.
The main purpose of this note is the study of the total space of a holomorphic Lie algebroid . The paper is structured in three parts. In the first section we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The se…
We introduce logarithmic Picard algebroids, a natural class of Lie algebroids adapted to a simple normal crossings divisor on a smooth projective variety. We show that such algebroids are classified by a subspace of the de Rham cohomology of the divisor complement determined by its mixed Hodge structure. We then solve …
We introduce Courant algebroids, providing definitions, some historical notes, and some elementary properties. Next, we summarize basic properties of graded manifolds. Then, drawing on the work of Roytenberg and others, we introduce the graded or supergraded language demonstrating a cochain complex / cohomology for (ge…
For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string effective actions, the situation becomes more complicated due to the presence of t…
We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.
Hypercomplex structures on Courant algebroids unify holomorphic symplectic structures and usual hypercomplex structures. In this note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree…
Computes colored HOMFLYPT invariants using holomorphic curves.