Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring

TL;DR

This paper explores the dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring in type IIA theory, deriving the action, analyzing quantum corrections, and comparing string energies with Bethe ansatz predictions, revealing integrable structures and reflectionless scattering.

Contribution

It provides a detailed near BMN expansion of the superstring action, verifies one-loop finiteness, and compares string energies with Bethe equations, highlighting integrability and scattering properties.

Findings

Two-point functions are one-loop finite.

Perfect agreement with Bethe equations in certain sectors.

The worldsheet S-matrix is reflectionless.

Abstract

We investigate the type IIA AdS(3) x S(3) x M(4) superstring with M(4)=S(3) x S(1) or M(4)=T(4). String theory in this background is interesting because of AdS3/CFT2 and its newly discovered integrable structures. We derive the kappa symmetry gauge-fixed Green-Schwarz string action to quadratic order in fermions and quartic order in fields utilizing a near BMN expansion. As a first consistency check of our results we show that the two point functions are one-loop finite in dimensional regularization. We then perform a Hamiltonian analysis where we compare the energy of string states with the predictions of a set of conjectured Bethe equations. While we find perfect agreement for single rank one sectors, we find that the product SU(2) x SU(2) sector does not match unless the Bethe equations decouple completely. We then calculate 2 to 2 bosonic tree-level scattering processes on the string worldsheet and show that the two-dimensional S-matrix is reflectionless. This might be important due to the presence of massless worldsheet excitations which are generally not described by the Bethe equations.