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

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.

UV divergences, RG equations and high energy behaviour of the amplitudes in the Wess-Zumino model with quartic interaction

“…This implies that the logarithms we have summed up can be interpreted as IR logarithms, i.e. that formulas (6.11) describe the IR behaviour of the amplitude up to some scale ∼ 1/g [30,32]. This interpretation, as well as the structure of the expressions themselves, is close to the interpretation of the standard RG logarithms resummation in renormalizable theories within the context of critical behaviour [23].…”