Representation theory and integration of nonlinear spherically symmetric equations to gauge theories

Abstract

A constructive proof of complete integrability of spherically symmetric self-dual equations in Euclidean space R^ for an arbitrary embedding of SU(2) in an arbitrary gauge group G is given on the base of Lax-type representation and representation theory. The equations are solved explicitly for the case of simple Lie groups G.

A BRST operator for non-critical W-strings

“…Thus, in addition to the well-known generalizations to super-geometry, one can also try to construct a "Wgeometry" [8] in which W -gravity is coupled to conformal W -matter [9][10][11]. One expects that such a theory is governed by a Toda system that extends the Liouville theory of two-dimensional gravity (see, for example, [12]). In a sense, this generalization consists in replacing SL(2) by some other semi-simple Lie group G ⋆ .…”

From two-dimensional conformal to four-dimensional self-dual theories: Quaternionic analyticity

“…It must also be mentioned that intimate connections of these theories to various one-and two-dimensional integrable systems were discussed more than ten years ago already, e.g. [23], [24], [25]. A suggestion was even made [26], [27] that all integrable systems might be deduced by dimensional reduction from the 4D self-dual theories, inheriting their remarkable properties.…”

Generalized pohlmeyer transformation — Some nonlinear systems with exponential interactions

“…(9) any nonlinear equation with the exponential interaction and expression (6) gives a solution of this equation. The function u, parametrizing this solution, is not an arbitrary holomorphic function, but satisfies some constraints.…”