Singularities of the magnon boundstate S-matrix

Abstract

We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N = 4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.

Resurgence of the dressing phase for AdS5 × S5

“…The weak coupling expansion for σ was conjectured in [14] (BES) as a sort of analytic continuation of the corresponding strong coupling expansion. In opposite to the latter, the weak coupling expansion of θ(x 1 , x 2 ) has a finite radius of convergence and defines a function which admits an integral representation (DHM) well defined in a certain kinematical region of particle rapidities x 1 , x 2 and for finite values of g [15]. Analytic continuation of the dressing phase to other kinematical regions compatible with crossing symmetry has been constructed in [16], which in fact provides verification of the crossing equation for finite g. Finally, under some assumptions on the analytic structure the minimal solution of the crossing equation has been found and cast precisely in the DHM form [17,18].…”

Wrapping interactions at strong coupling: The giant magnon

“…In addition there are various conventions for the S-matrix (see e.g. [20]). As in the case of the magnon calculation presented in the remaining part of the paper we will justify our choices a-posteriori by the final result.…”

“…So it is also interesting to independently test as large part of this solution as possible. A 2-loop test has been performed in the near-flat space limit in [19], while the considerations in [20] on the location of double poles involve the full expression. As a byproduct, the present paper provides a stringent test sensitive to all even loop orders at strong coupling.…”

Dressing phases ofAdS3/CFT2

“…In the context of the AdS 5 /CFT 4 integrable system, crossing symmetry constraints were first identified in [8]. The solution of these constraints [9][10][11][12][13][14], the so-called dressing phase, conventionally written as σ ≡ e iθ , is a key ingredient in matching the strong and weak coupling limits of the dualilty [15].…”