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.
Highlights
Analytically in two dimensions [1] and it was found that the theories which maximize various couplings have no particle production
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 results here were the outcome of our explorations at the 2017 Perimeter Institute Winter School
Summary
We tie up the two loose ends of the discussion above. First, we discuss in more detail the seeds of the recursion relations, i.e. the remarkable identities which state that particular sums of diagrams arising in lower-point amplitudes add up to constants. We explain in more detail why, once this is established, we are guaranteed to be able to cancel higher-particle production by suitably adjusting the remaining interaction vertices
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