The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as ‘master dispersionless systems’ in four and three dimensions respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In parti...

We determine set-theoretic defining equations for the variety Dualk,d,N ⊂ P(S d C N ) of hypersurfaces of degree d in C that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety GLn2 · [detn] ⊂ P(S n C n2), showing it is an irreducible component of the variety of hypersurfaces of degree n in C 2 with dual of dimension at most 2n − 2. We establish add...

The path-integral approach to quantum field theory assigns special importance to finite action Euclidean solutions of classical field equations. In Yang-Mills gauge theories, the instanton solutions of classical field equations with self-dual field strength have given rise to a new, nonperturbative treatment of the quantum field theory and its vacuum state. Since gravitation is also a species o...

We study the system of self-dual Maxwell field coupled to 3D gravity with torsion, with Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central charges, and gives a simple correspondence between self-dual solutions with torsion and their Riemannian counterparts. We construct two exact self-dual solutions,...

The relation between two–dimensional integrable systems and four–dimen-sional self–dual Yang–Mills equations is considered. Within the twistor description and the zero–curvature representation a method is given to associate self–dual Yang-Mills connections with integrable systems of the Korteweg–de Vries and non–linear Schrödinger type or principal chiral models. Examples of self–dual connectio...

We study the equations of motion of fermions in type IIB supergravity in the context of the gauge/gravity correspondence. The main motivation is the search for normalizable fermionic zero modes in such backgrounds, to be interpreted as composite massless fermions in the dual theory. We specialize to backgrounds characterized by a constant dilaton and a self-dual three-form. In the specific case...

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge elds and derive the Bogomol'nyi-type bound. We nd all possible cylindrically symmetric vortex solutions and vortex-particle composites by examining the Einstein equations and the rstorder Bogomol'nyi equations. The underlying spatia...

We look for 3–dimensional Poisson–Lie dualizable sigma models that satisfy the vanishing β–function equations with constant dilaton field. Using the Poisson–Lie T–plurality we then construct 3–dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for “traceless” dual algebras they satisfy the van...

We employ a conditional event study methodology to determine if dual traders in futures markets are informed traders. Underpinning this approach is the assumption that a dual trader’s decision to trade on her own account is not random, but is endogenously determined by her expectations of profit related to this decision. Therefore, the appropriate empirical framework to analyze the issue is a s...

We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters whose evolution are governed by the corresponding-order dual cumulant (dual semi-invariant) of the evolution operators of finitely many par...