Related papers: WDVV Equations from Algebra of Forms
We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex…
We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…
In the theory of quantum cohomologies the WDVV equations imply integrability of the system $(I\partial_\mu - zC_\mu)\psi = 0$. However, in generic situation -- of which an example is provided by the Seiberg-Witten theory -- there is no…
We organize and review some material from various sources about prepotentials, Riemann surfaces and kernels, WDVV, and the renormalization group, provide some further connections and information, and indicate some directions and problems.
We define an almost periodic extension of the Wiener algebras in the quaternionic setting and prove a Wiener-Levy type theorem for it, as well as extending the theorem to the matrix-valued case. We prove a Wiener-Hopf factorization theorem…
In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop algebra of $\mathfrak{sl}(2)$, and employs a family of…
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…
This paper introduces and systematically studies Weyl-type, Witt-type, and non-associative algebras defined over expolynomial rings -- commutative rings generated by exponential functions $e^{\alpha x}$, exponentials of exponentials $e^{\pm…
We show that Witten-Dijkgraaf-Verlinde-Verlinde equation underlies the construction of N=4 superconformal multi--particle mechanics in one dimension, including a N=4 superconformal Calogero model.
In this talk I describe some applications of random matrix models to the study of N=1 supersymmetric Yang-Mills theories with matter fields in the fundamental representation. I review the derivation of the…
The vector Riemann-Hilbert problem is analyzed when the entries of its matrix coefficient are meromorphic and almost periodic functions. Three cases for the meromorphic functions, when they have (i) a finite number of poles and zeros…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We construct second order reductions of the generalized Witten-Dijkgraaf-Verlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction.
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…
We give a family of solutions of Witten-Dijkgraaf-Verlinde-Verlinde equations in $n$-dimensional space. It is defined in terms of $BC_{n}$ root system and $n+2$ independent multiplicity parameters. We also apply these solutions to define…
We give a computability result for open Gromov-Witten invariants based on open WDVV equations. This is analogous to the result of Kontsevich-Manin for closed Gromov-Witten invariants. For greater generality, we base the argument on a formal…
We first recall Solomon's relations for Welschinger's invariants counting real curves in real symplectic fourfolds, announced in \cite{Jake2} and established in \cite{RealWDVV}, and the WDVV-style relations for Welschinger's invariants…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which…
Rational solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations of associativity are given in terms a configurations of vectors which satisfy certain algebraic conditions known as $\bigvee$-conditions. The simplest examples…