The bound state S-matrix for superstring

Abstract

Abstract:We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS 5 × S 5 . The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function 4 F 3 . We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Lüscher approaches to the finite-size spectral problem. They also shed some light on the construction of the universal R-matrix for the centrally-extended psu(2|2) superalgebra.

On Yangian and long representations of the centrally extended $ \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) $ superalgebra

“…We recall that this construction proved to work well for the fundamental or bound-state, i.e. short, representations, and it lead to the complete determination of the corresponding bound state scattering matrix [35,42]. However, where…”

“…In many respects the success of this research is based on the existence of an asymptotic symmetry, which consists of (two copies of) the su(2|2) superalgebra [31][32][33] centrally extended by two central charges. In particular, this superalgebra and the associated Yangian [34] have been used to explicitly determine the S-matrices describing scattering of fundamental and bound-state particles of the light-cone string sigma model [35,36], which is important for setting up the Thermodynamic Bethe Ansatz approach.…”

A next-to-leading Lüscher formula

“…Moreover, Λ Q 1 ,Q 2 SU(2|2) is the diagonalized SU(2|2)-invariant S-matrix for the scattering between two generic mirror bound-states [53], and U Q 1 ,Q 2 SU(2|2) is its change of basis matrix. In order to calculate the finite-size correction to the 8-loop anomalous dimension of the Konishi operator one needs just formulas (5.5) and (5.7), with a = 1, j = 1, 2, p 1 = −p 2 = 2π/3, together with the leading order formulas of [9] for energy and rapidities' corrections, expanded to g 16 .…”

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

“…By solving the reflection intertwining equation for all Lie algebra and Yangian symmetries, 26) one can obtain all reflection coefficients of any bound-state reflection matrix up to the overall dressing phase. This could be done in a similar way as it was done for the boundstate S-matrix in [10]. However, due to very bulky form of the boundary Yangian, this would be extremely challenging.…”

“…One of the key directions of this exploration is the worldsheet scattering, which is largely driven by the centrally extended psu (2|2) C algebra [2][3][4] and its Yangian extension [5]. These algebras play a central role in finding the relevant scattering matrices and writing the corresponding Bethe ansatz equations [6][7][8][9][10]. This data is also of particular importance in solving the so-called T -and Y -systems used to describe the spectral problem [11] and calculating Wilson loops [12].…”