Related papers: Quantum Master Equation and Open Gromov-Witten the…
We define a new Gromov-Witten theory relative to simple normal crossing divisors as a limit of Gromov-Witten theory of multi-root stacks. Several structural properties are proved including relative quantum cohomology, Givental formalism,…
We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L \subset X$ with a bounding chain. Simultaneously, we define the…
Let $(X,E)$ be a smooth log Calabi-Yau pair consisting of a smooth Fano surface $X$ and a smooth anticanonical divisor $E$. We obtain certain higher genus local Gromov-Witten invariants from the projectivization of the canonical bundle $Z…
In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…
An effective algorithm of determining Gromov--Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov--Witten invariants of the ambient space is proposed. The Appendix is joint with E. Schulte-Geers.
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We explicitly calculate some Gromov--Witten correspondences determined by maps of labeled curves of genus zero to the moduli spaces of labeled curves of genus zero. We consider these calculations as the first step towards studying the…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent potential in genus 0 of an arbitrary conformal Frobenius…
The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the…
We investigate the problem of what evolutions an open quantum system described by a time-local Master equation can undergo with universal coherent controls. A series of conditions are given which exclude channels from being reachable by any…
We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.
Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces is a long standing open…
In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is…
We use Pixton's relations to prove a reconstruction theorem for genus 2 Gromov-Witten invariants in the style of Kontsevich-Manin (genus 0) and Getzler (genus 1). We also calculate genus 2 (descendant) Gromov-Witten invariants of…
We study the effective Batalin-Vilkovisky quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals…
We prove the finite generation conjecture of arXiv:hep-th/0406078 for the Gromov-Witten potentials of the Calabi-Yau hypersurfaces $Z_6 \subset \mathbb{P}(1,1,1,1,2)$, $Z_8 \subset \mathbb{P}(1,1,1,1,4)$, and $Z_{10} \subset…
We describe generating functions for arbitrary-genus Gromov-Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing…