Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
Nitin Rughoonauth, Per Sundin, Linus Wulff
TL;DR
The paper constructs and analyzes the Green–Schwarz superstring in AdS$_3\times$S$^3\times$S$^3\times$S$^1$ with RR flux, using a near-BMN expansion to quartic order in fields and quadratic order in fermions. It delivers the GS action, investigates kappa-symmetry gauge fixing, and demonstrates one-loop finiteness of two-point functions, providing a nontrivial consistency check. A Hamiltonian analysis compares string energies to conjectured Bethe equations, finding exact agreement for rank-one SU(2) sectors but a mismatch in the SU(2)×SU(2) sector unless the length parameter decouples between sectors, suggesting two effectively independent spin chains. The tree-level bosonic S-matrix is computed and shown to be reflectionless, highlighting the special role of massless worldsheet modes and signaling subtleties for incorporating them into an exact Bethe ansatz.
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.