111 research outputs found
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
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