Related papers: Quantum BCOV theory on Calabi-Yau manifolds and th…
For a Calabi-Yau manifold $X$, the Kawamata - Morrison movable cone conjecture connects the convex geometry of the movable cone $\overline{\mathrm{Mov}}(X)$ to the birational automorphism group. Using the theory of Coxeter groups, Cantat…
Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. Of particular interest are driven conformal field theories (CFTs) which describe quantum many-body systems at criticality. In this paper, we…
We relate graph complexes, Calabi-Yau $A_\infty$-categories and Kontsevich's cocycle construction. Our main result produces a commutative square of shifted Poisson algebras; one of its edges is the Loday-Quillen-Tsygan map, generalized to…
We propose an alternative description of 2 dimensional Conformal Field Theory in terms of Quantum Inverse Scattering. It is based on the generalized KdV systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as Poisson…
This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting…
This paper is devoted to a discussion of Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties is revisited by using GWW-classes and it is…
The Gopakumar-Vafa (GV) formula expresses certain couplings that arise in Type IIA compactification to four dimensions on a Calabi-Yau manifold in terms of a counting of BPS states in M-theory. The couplings in question have applications to…
We formulate the quantum field theory description of neutron-antineutron oscillations in the framework of canonical quantization, in analogy with the Bardeen--Cooper--Schrieffer (BCS) theory and the Nambu--Jona-Lasinio model. The physical…
We give a short new computation of the quantum cohomology of an arbitrary smooth toric variety $X$, by showing directly that the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono defines an isomorphism onto a suitable Jacobian ring. The proof is…
We derive the quantum analogue of a B\"acklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schr\"odinger equation. The quantisation of the Ablowitz-Ladik chain leads to the $q$-boson model.…
We generalize the cohomological mirror duality of Borcea and Voisin in any dimension and for any number of factors. Our proof applies to all examples which can be constructed through Berglund-H\"{u}bsch duality. Our method is a variant of…
The paper is devoted to the formulation of quantum field theory for an early universe in General Relativity considered as the Dirac general constrained system. The main idea is the Hamiltonian reduction of the constrained system in terms of…
Quantum Cosmology and Gravity are formulated here as the primary and secondary quantizations of the energy constraints by analogy with the historical formulation of quantum field theory. New fact is that both the Universe and its matter are…
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…
We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a…
The main purpose of this article is to discuss a project relating Gopakumar-Vafa invariants to quantum K-invariants on Calabi-Yau threefolds. Results in genus zero, including recent and forthcoming works, are reported.
A version of the Donaldson-Thomas invariants of a Calabi-Yau threefold is proposed as a conjectural mathematical definition of the Gopakumar-Vafa invariants. These invariants have a local version, which is verified to satisfy the required…
We use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum…
In this paper, making use of the global one-dimensionality conjecture, we discuss the reduction of the Wheeler-DeWitt quantum geometrodynamics to the Klein-Gordon equation describing the scalar bosonic particle. The method of second…
We study some arithmetic properties of the mirror maps and the quantum Yukawa coupling for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to…