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

Abstract

We consider a general (beyond $T\bar{T}$) deformation of the 2D $O(N+1)$ $\sigma$-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 $2\to 2$ scattering amplitude and provide the exact result for the $2\to 2$ $S$-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 $T\bar{T}$ deformation.

Comments: 22 pages, 1 figure; The erroneous expressions for the tree-level LL-coefficients were corrected