No Particle Production in Two Dimensions: Recursion Relations and Multi-Regge Limit

TL;DR

This paper develops recursion relations for two-dimensional quantum field theories with no particle production, unifying several models like sine-Gordon and Toda theories through high-energy limits.

Contribution

It introduces a novel method using high-energy limits to derive recursion relations that determine couplings in 2D QFTs with no particle production, unifying multiple models.

Findings

Recursion relations fix couplings in 2D QFTs.

Models like sine-Gordon and Toda theories are recovered.

Method simplifies understanding of integrable 2D theories.

Abstract

We introduce high-energy limits which allow us to derive recursion relations fixing the various couplings of Lagrangians of two-dimensional relativistic quantum field theories with no tree-level particle production in a very straightforward way. The sine-Gordon model, the Bullough-Dodd theory, Toda theories of various kinds and the U(N) non-linear sigma model can all be rediscovered in this way. The results here were the outcome of our explorations at the 2017 Perimeter Institute Winter School.