A method of exact all-order summation of leading infrared logarithms in two dimensional massless Φ 4 -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 E 2 ln(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.

We consider a general (beyond $$ T\overline{T} $$ T T ¯ ) deformation of the 2D O(N + 1) σ-model by the irrelevant dimension-four operators. The theory deformed in this most general way is not integrable, and the S-matrix loses its factorization properties. We perform the all-order summation of the leading infrared logs for the 2 → 2 scattering amplitude and provide the exact result for the 2 → 2 S-matrix in the leading logarithmic approximation. These results can provide us with new insights into the properties of the theories deformed by irrelevant operators more general than the $$ T\overline{T} $$ T T ¯ deformation.

A correction to this paper has been published: https://doi.org/10.1007/JHEP05(2021)266