Worldsheet scattering in AdS(3)/CFT(2)

We confront the recently proposed exact S-matrices for AdS(3)/CFT(2) with direct worldsheet calculations. Utilizing the BMN and Near Flat Space (NFS) expansions for strings on AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) we compute both tree-level and one-loop scattering amplitudes. Up to some minor issues we find nice agreement in the tree-level sector. At the one-loop level however we find that certain non-zero tree-level processes, which are not visible in the exact solution, contribute, via the optical theorem, and give an apparent mismatch for certain amplitudes. Furthermore we find that a proposed one-loop modification of the dressing phase correctly reproduces the worldsheet calculation while the standard Hernandez-Lopez phase does not. We also compute several massless to massless processes.Comment: 20 pages, 1 figure; v2: Some clarifications in comparison to literatur

The complete one-loop BMN S-matrix in AdS(3) x S(3) x T(4)

We compute the full one-loop 2-particle S-matrix for excitations of the type IIB AdS(3) x S(3) x T(4) BMN string. The S-matrix is found to respect the expected symmetries and the phases are consistent with the crossing equations. By analyzing how the relevant integrals scale with the IR regulator we show that scattering of massless bosons is trivial at two loops. Based on our results we argue that the additional su(2) S-matrix appearing in the massless sector in the exact solution should trivialize.Comment: 20 pages; v2: References and minor clarification adde

The AdS(n) x S(n) x T(10-2n) BMN string at two loops

We calculate the two-loop correction to the dispersion relation for worldsheet modes of the BMN string in AdS(n) x S(n) x T(10-2n) for n=2,3,5. For the massive modes the result agrees with the exact dispersion relation derived from symmetry considerations with no correction to the interpolating function h. For the massless modes in AdS(3) x S(3) x T(4) however our result does not match what one expects from the corresponding symmetry based analysis. We also derive the S-matrix for massless modes up to the one-loop order. The scattering phase is given by the massless limit of the Hernandez-Lopez phase. In addition we compute a certain massless S-matrix element at two loops and show that it vanishes suggesting that the two-loop phase in the massless sector is zero.Comment: 30 pages, 6 figures; v2: References and comment on type IIB added, acknowledgements updated; v3: Comparison to proposed exact massless S-matrix in sec 5.3 corrected. Only non-trivial phase appears at one loop. Additional minor clarification

Classical and quantum integrability in AdS 2/CFT 1

We investigate the type IIA string on AdS 2 × S 2 × T 6 supported by RR-flux which describes the gravitational side of the AdS 2/CFT 1 correspondence. While the four-dimensional part AdS 2 × S 2 can be realized as a supercoset, the full superstring has both coset and non-coset excitations, the latter giving rise to massless worldsheet modes, a somewhat novel feature in AdS/CFT. The string is nevertheless known to be integrable at the classical level. In this paper we perform several computations checking aspects of both classical and quantum string integrability. At the classical level we compute energies for the near BMN string and successfully match these against Bethe ansatz predictions. Furthermore, integrability dictates a magnon dispersion relation which we compare with the poles of loop corrected propagators, at both the one and two-loop level. At one loop, where only tadpole diagrams contribute, we find that the bosonic and fermionic contributions sum up to zero. Under the assumption of worldsheet supersymmetry, we then compute the two-loop sunset diagram in the near flat space limit. As in AdS 5 × S 5 we find that the result fits nicely into the sine-square structure of the dispersion relation

The low energy limit of the AdS 3 × S 3 × M 4 spinning string

We derive the low-energy effective action for the spinning (GKP) string in AdS(3) x S(3) x M(4) where M(4) = S(3) x S(1) or T(4). In the first case the action consists of two O(4) non-linear sigma models which are coupled through their interaction with four massless Majorana fermions (plus one free decoupled scalar). While in the second case it consists of one O(4) sigma model coupled to four Majorana fermions together with four free scalars from the T(4). We show that these models are classically integrable by constructing their Lax connections.Comment: 13 page