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

Abstract: In this talk we consider the most 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 way is generally not integrable, and its $S$-matrix loses the factorization properties.  We present an overview of the method of exact all-order summation of leading infrared  logarithms in $2D$ massless $\phi^4$-type non-renormalizable effective field theories (EFTs).  It is based on the fundamental requirements of unitarity, analyticity and crossing symmetry of scattering amplitudes and generalizes the renormalization group technique for the case of non-renormalizable EFTs.   This method allows us to provide the exact results for the  $2 \to 2$ $S$-matrix in the leading logarithmic  approximation in the deformed $2D$ $O(N+1)$ $\sigma$-model. In particular, we present the remarkable solution  expressed in terms of elliptic functions leading to scattering amplitudes with a doubly periodic structure of the Landau  poles. We discuss the new insights into the properties of the theories deformed by irrelevant operators more general than  the $T\bar{T}$ deformation from the perspective of our approach.TBA

HEP - theory

Audience: researchers in the topic

Exact Results on Irrelevant Deformations of QFTs

Series comments: The registration for online participants is now open. www.apctp.org/theme/d/html/activities/activities01-1_read.php?id=1549&page=1