On the massless tree-level S-matrix in 2d sigma models

Abstract

Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d σ-models expanded near the trivial vacuum. We find that, in contrast to the standard massive case, there is no apparent link between massless S-matrices and integrability: in well-known integrable models the tree-level massless S-matrix fails to factorize and exhibits particle production. Such tree-level particle production is found in several classically integrable models: the principal chiral model, its classically equivalent "pseudo-dual" model, its non-abelian dual model and also the SO(N +1)/SO(N ) coset model. The connection to integrability may, in principle, be restored if one expands near a nontrivial vacuum with massive excitations. We discuss IR ambiguities in 2d massless tree-level amplitudes and their resolution using either a small mass parameter or the i -regularization. In general, these ambiguities can lead to anomalies in the equivalence of the S-matrix under field redefinitions, and may be linked to the observed particle production in integrable models. We also comment on the transformation of massless S-matrices under σ-model T-duality, comparing the standard and the "doubled" formulations (with T-duality covariance built into the latter). 1 bhoare@ethz.ch 2 n.

On the Hamiltonian formulation, integrability and algebraic structures of the Rajeev-Ranken model

“…If we postulate the canonical PBs (14). The canonical PBs between f and π imply the following PBs among the currents I, J and f:…”

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An Introduction to Generalised Dualities and their Applications to Holography and Integrability

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