Near BMN dynamics of the AdS 3 × S 3 × S 3 × S 1 superstring

Abstract

We investigate the type IIA AdS 3 × S 3 × M 4 superstring with M 4 = S 3 × S 1 or M 4 = T 4 . String theory in this background is interesting because of AdS 3 /CF T 2 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)×SU (2) sector does not match unless the Bethe equations decouple completely. We then calculate 2 → 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.arXiv:1204.4742v3 [hep-th]

Dressing phases ofAdS3/CFT2

“…This is in agreement with an explicit strongcoupling regime calculation done in [34,36,38]. At the HL-order, our phases are different from one another, confirming that the system does have two distinct dressing phases.…”

“…Expanding on this, in [32] the exact integrable S-matrix and associated Bethe Ansatz of the integrable system associated to Type IIB string theory on AdS 3 ×S 3 ×T 4 with R-R flux was constructed. 3 A number of recent papers have performed important perturbative calculations for string theory on AdS 3 backgrounds [26,[34][35][36][37][38][39][40]. Further, the integrability of a family of AdS 3 × S 3 × T 4 theories with both R-R and NS-NS flux has been investigated [41].…”

The AdS n × S n × T 10−2n BMN string at two loops

“…1 The reason for this is that in these models one has only even order interaction vertices in the BMN expansion. In particular there are no cubic interactions which leads to a big reduction in the number of possible Feynman diagrams compared to other cases such as AdS 4 × CP 3 and AdS 3 × S 3 × S 3 × S 1 [8,9].…”

“…Therefore calculations were done either in the so-called Near-Flat-Space limit [10][11][12][13][14][15], using generalized unitarity [16][17][18] or by computing only quantities that were explicitly finite [4,9,19,20]. Thus one could side-step the issue of regularization.…”

“…For general masses m, M these recursion relations allow us to solve for integrals of the type I r0s0 in terms of integrals of the type I r000 , which 9 Here we have used shifts of the loop variable in the tadpole integrals that appear and the fact that T rs m = 0 for r = s by Lorentz-invariance. 10 To compute for example the wave function renormalization at two loops one would need to evaluate the sunset integrals off-shell.…”