On the massless tree-level S-matrix in 2d sigma models. (14th March 2019)

• Record Type: Journal Article
• Authors: Hoare, Ben; Levine, Nat; Tseytlin, Arkady A
• Is Part Of: Journal of physics. Volume 52:Number 14(2019)
• Publication Date: 2019-03-14
• Subjects: string sigma models -- integrability -- massless S-matrix; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab0b79
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d -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 coset model. The connection to integrability may, in principle, be restored if one expands near a non-trivial 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 -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 -model T-duality, comparing the standard and the 'doubled' formulations (with T-duality covariance built into the latter).