From nesting to dressing

Understand

In integrable field theories the S-matrix is usually a product of a relatively simple matrix and a complicated scalar factor.

• We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz.
• We formulate a proposal, up to some discrete ambiguities, how to reconstruct the scalar factor from the nested Bethe equations and check it for several relativistic integrable field theories.
• We then apply this proposal to the AdS asymptotic Bethe ansatz and recover the dressing factor in the integral representation of Dorey, Hofman and Maldacena.