  The near-collinear expansion of scattering amplitudes in maximally
supersymmetric Yang-Mills theory at strong coupling is governed by the dynamics
of stings propagating on the five sphere. The pentagon transitions in the
operator product expansion which systematize the series get reformulated in
terms of matrix elements of branch-point twist operators in the two-dimensional
O(6) nonlinear sigma model. The facts that the latter is an asymptotically free
field theory and that there exists no local realization of twist fields
prevents one from explicit calculation of their scaling dimensions and operator
product expansion coefficients. This complication is bypassed making use of the
equivalence of the sigma model to the infinite-level limit of WZNW models
perturbed by current-current interactions, such that one can use conformal
symmetry and conformal perturbation theory for systematic calculations.
Presently, to set up the formalism, we consider the O(3) sigma model which is
reformulated as perturbed parafermions.
