Two-dimensional S-matrices from unitarity cuts

TL;DR

This paper uses unitarity methods to compute one-loop 2->2 scattering S-matrices in various two-dimensional models, revealing differences between supersymmetric and non-supersymmetric integrable theories and confirming results for the AdS_5 x S^5 superstring.

Contribution

It introduces a method to derive one-loop S-matrices from tree-level amplitudes in 2D models, highlighting the role of supersymmetry and integrability in the cut-constructibility of these matrices.

Findings

Supersymmetric models have cut-constructible one-loop S-matrices.

Non-supersymmetric integrable models have rational terms proportional to the tree-level S-matrix.

The method reproduces known S-matrix results for the AdS_5 x S^5 superstring at one-loop.

Abstract

Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories, finding evidence that for supersymmetric models the one-loop S-matrix is cut-constructible, while for models without supersymmetry (but with integrability) the missing rational terms are proportional to the tree-level S-matrix and therefore can be interpreted as a shift in the coupling. Finally, applying our procedure to the world-sheet theory for the light-cone gauge-fixed AdS_5 x S^5 superstring we reproduce, at one-loop in the near-BMN expansion, the S-matrix known from integrability techniques.