Related papers: A Lecture on Holomorphic Anomaly Equations and Ext…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
We found Bogomol'nyi type of the first order differential equations in three dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these…
Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Kodaira-Spenser theory (we call it the BCOV theory). This is the…
In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly…
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. It is shown that the Cauchy problem for these equations is well-posed with data consisting of the limiting…
Minimal BCOV theory is a classical field theory which describes a subclass of deformations of the category of perfect complexes on a Calabi-Yau variety. We compute minimal models for $L_\infty$-algebras describing minimal BCOV theory and…
The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give…
We consider various notions of holomorphic extendability of complex valued functions defined on subsets of $\mathbf C^n$, including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic…
In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.
The present paper is devoted to the study of semi-linear Beltrami equations which are closely relevant to the corresponding semi-linear Poisson type equations of mathematical physics on the plane in anisotropic and inhomogeneous media. In…
We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries…
A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…
Field theory including Supersymmetry and Bose Fermi Symmetry is an active subject of particle physics and cosmology. Recent and expected observational evidence gives indicators for the creation and destruction of normal and supersymmetric…
Recent experiments on Brownian colloidal particles have been studied theoretically in terms of overdamped Langevin equations with multiplicative white noise using an unconventional stochastic interpretation. Complementary numerical…
We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii-Teissier inequalities.
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
Interrelation between Thom's catastrophes and differential equations revisited. It is shown that versal deformations of critical points for singularities of A,D,E type are described by the systems of Hamilton-Jacobi type equations. For…
We propose a recipe - arguably the simplest - to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants…
By using algebraic tools from differential Gerstenhaber algebras and Batalin-Vilkobisky algebras, we provide a new perspective on the modular class in Poisson geometry and the intrinsic biderivation of a Lie bialgebra. Furthermore,…
Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau…