Related papers: QCD, Wick's Theorem for KdV $\tau$-functions and t…
We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral…
We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity,…
We study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given by shifted symmetric functions. The proof is based on the…
We present a new construction related to systems of polynomials which are consistent on a cube. The consistent polynomials underlie the integrability of discrete counterparts of integrable partial differential equations of Korteweg- de…
The partition function of two dimensional QCD on a Riemann surface of area $A$ is expanded as a power series in $1/N$ and $A$. It is shown that the coefficients of this expansion are precisely determined by a sum over maps from a two…
Quantum differential operators on Reflection Equation Algebras, corresponding to Hecke symmetries R were introduced in previous publications. In the present paper we are mainly interested in quantum analogs of the Laplace and Casimir…
We study the supersymmetric quantum dynamics of the cosmological models obtained by reducing $D=5$ supergravity to one timelike dimension. This consistent truncation has fourteen bosonic degrees of freedom, while the quantization of the…
Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian operators for integrable systems can be constructed using Dirac's theory of constraints. We illustrate this by giving a systematic discussion of the first…
We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the $\epsilon$-regime. The fermion determinant is approximated by a truncated product of low-lying eigenvalues of the overlap-Dirac operator. With…
We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel/Nijhoff] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev/Volkov]. The difference of these…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
The Korteweg-de Vries equation (KdV) and various generalized, most often semi- linear versions have been studied for about 50 years. Here, the focus is made on a quasi-linear generalization of the KdV equation, which has a fairly general…
A generalisation of the non--perturbatively stable solutions of string equations which respect the KdV flows, obtained recently for the $(2m-1,2)$ conformal minimal models coupled to two--dimensional quantum gravity, is presented for the…
It was suggested in hep-th/0002106, that semiclassically, a partition function of a string theory in the 5 dimensional constant negative curvature space with a boundary condition at the absolute satisfy the loop equation with respect to…
The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously proposed and developed for Yang--Mills theory in Coulomb gauge, is generalized to full QCD. For…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
We define twisted versions of the classical and quantum double ramification hierarchy construction based on intersection theory of the strata of meromorphic differentials in the moduli space of stable curves and $k$-twisted double…
Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be…
Using the well-known result for the fermionic determinant in terms of a WZW theory, we write QCD$_2$ in bosonized form. After some manipulations we give two versions of the theory, where it is factorized as a product of the conformally…
The possibility that QED and recently developed non-Hermitian, or magnetic, versions of QED are equivalent is considered. Under this duality the Hamiltonians and anomalous axial currents of the two theories are identified. A consequence of…