Two-dimensional S-matrices from unitarity cuts

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.Comment: 23 pages, 1 figure; v2: 24 pages, minor corrections, reference and note added; v3: minor typos correcte

Dressing phases ofAdS3/CFT2

“…The logarithmic part agrees 16 with what conjectured in [36], also in agreement with recent results found by unitarity techniques [39,40]. The discrepancy in the rational part may come from the fact that the Bethe ansatz assumed in [36] differs from the one of [32] by terms of the form 1 − 1…”

“…Expanding on this, in [32] the exact integrable S-matrix and associated Bethe Ansatz of the integrable system associated to Type IIB string theory on AdS 3 ×S 3 ×T 4 with R-R flux was constructed. 3 A number of recent papers have performed important perturbative calculations for string theory on AdS 3 backgrounds [26,[34][35][36][37][38][39][40]. Further, the integrability of a family of AdS 3 × S 3 × T 4 theories with both R-R and NS-NS flux has been investigated [41].…”

Resurgence of the dressing phase for AdS5 × S5

“…The S-matrix computed from the sigma model perturbation theory has been shown (see e.g. [34,35]) to reproduce the well known first few orders of the dressing phase expansion. For this reason and from the presence of non-perturbative terms in the dressing phase transseries expansion, we predict the existence of new non-perturbative objects in the world-sheet sigma model theory 1 (or possibly a suitable complexification thereof) that hopefully one can construct more easily in one of the Pohlmeyer reduced versions of the world-sheet theory [36].…”

The AdS n × S n × T 10−2n BMN string at two loops

“…Therefore calculations were done either in the so-called Near-Flat-Space limit [10][11][12][13][14][15], using generalized unitarity [16][17][18] or by computing only quantities that were explicitly finite [4,9,19,20]. Thus one could side-step the issue of regularization.…”