Two-dimensional Sl Research Articles

Correlation functions in conformal Toda field theory I

Two-dimensional sl(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the three-point correlation functions of the exponential fields if one of the three fields has a special form. In this case it is possible to write down and solve explicitly the differential equation for the four-point correlation function if the fourth field is completely degenerate. We give also expressions for the three-point correlation functions in the cases, when they can be expressed in terms of known functions. The semiclassical and minisuperspace approaches in the conformal Toda field theory are studied and the results coming from these approaches are compared with the proposed analytical expression for the three-point correlation function. We show, that in the framework of semiclassical and minisuperspace approaches general three-point correlation function can be reduced to the finite-dimensional integral.

Classification of vertex operators in two-dimensional sl(2,?)-invariant quantum field theory

Classification of vertex operators in two-dimensional sl(2,?)-invariant quantum field theory

An explicit form of the vertex operators in two-dimensional sl(2,?)-invariant field theory

An explicit form of the vertex operators in two-dimensional sl(2,ℂ)-invariant quantum field theory is found.

SL(3, R) 2 sigma-model related to the Dodd-Bullough equation

It is shown that the Dodd-Bullough equation in intimately connected with the nonlinear two-dimensional SL(3, R) sigma-model, the triplet of massless fields of which takes values on the sphere in the three-dimensional unimodular affine space. The equations of motion for the SL(3, R) sigma-model are written explicity.