Exact summation of leading logs around $$ T\overline{T} $$ deformation of O(N + 1)-symmetric 2D QFTs

Abstract

Abstract 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.