Exact Summation of Leading Logarithms in 2D Effective Field Theories

In the present work, we investigate low-energy leading logarithm approximation (LLA) of the binary scattering amplitudes in the 2D massless scalar purely non-renormalizable effective field theories. We concentrate on the method that allows one to derive a system of non-linear recurrence relations for the LLA coefficients. In the thesis, we apply this technique for the case of the SU(N)-symmetric bi-quartic model in the adjoint representation. In this model, we observe the ways to reduce the number of independent equations in the system. We consider the large-N limit and investigate approaches to the solution of the differential equations system on the generating functions (GF) for the LLA coefficients. In one of the special cases discussed, we obtain the GFs formulated in terms of the Weierstrass P- and zeta-functions. These GFs turn out to possess a doubly periodic structure of poles on the complex plane of the Mandelstam s variable, which can signify interesting for further investigation renormalization group properties of the theory.