Abstract
A method of exact all-order summation of leading infrared logarithms in two dimensional massless Φ4-type non-renormalizable effective field theories (EFTs) is developed. The method is applied to the O(N)-symmetric EFT, which is a two-dimensional sibling of the four dimensional O(N + 1)/O(N) sigma-model. For the first time the exact all-order summation of the (E2ln(1/E))n contributions (chiral logarithms) for the 2 → 2 scattering amplitudes is performed in closed analytical form. The cases when the resulting amplitudes turn to be meromorphic functions with an infinite number of poles (Landau poles) are identified. This provides the first explicit example of quasi-renormalizable field theories.
Highlights
Where Φa is the N -component scalar field, gab(Φ) is a metric on the SN -sphere of radius F which has the dimension of the mass
The method is applied to the O(N )-symmetric effective field theories (EFTs), which is a two-dimensional sibling of the four dimensional O(N + 1)/O(N ) sigma-model
We presented a general method for exact summation of leading logarithms in 2D nonrenormalizable EFTs
Summary
The differential equation (3.16) can be formally viewed as the equation of motion of a one dimensional mechanical system. The parameters M and δ of the equivalent mechanical system (4.5) turn out to be singular for N = 2. Summary of solutions for the mechanical system (4.3) expressed in terms of elliptic functions (and their degeneracies). For the case of the exponents of the potentials γ and δ equal to 0, 1, 2, 3, 4 the mechanical systems (4.3), (4.5) can be solved explicitly in terms of elliptic functions (or their degeneracies). The values of the corresponding theory parameters and a short summary of solutions is presented in tables 2, 3.
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