26 research outputs found
More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds
In this paper we continue the study, initiated in arXiv:1009.3498 and
arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings
in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum
contains non-supercoset worldsheet degrees of freedom corresponding to broken
supersymmetries in the bulk. We derive an explicit expression, to all orders in
the coset fermions and to second order in the non-coset fermions, which extends
the supercoset Lax connection in these backgrounds with terms depending on the
non-coset fermions. An important property of the obtained form of the Lax
connection is that it is invariant under Z_4-transformations of the
superisometry generators and the spectral parameter. This demonstrates that the
contribution of the non-coset fermions does not spoil the Z_4-symmetry of the
super-coset Lax connection which is of crucial importance for the application
of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and
AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a
very similar form. This is because their amount of target-space supersymmetries
complement each other to 32=24+8, the maximal number of 10d type II
supersymmetries. As a byproduct, this similarity has allowed us to obtain the
form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace
to all orders in the coset fermions and to the second order in the non-coset
ones.Comment: 28 pages; v2: References adde
Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
In this paper we continue the investigation of aspects of integrability of
the type IIA AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) superstrings.
By constructing a one parameter family of flat connections we prove that the
Green-Schwarz string is classically integrable, at least to quadratic order in
fermions, without fixing the kappa-symmetry. We then compare the quantum
dispersion relation, fixed by integrability up to an unknown interpolating
function h(lambda), to explicit one-loop calculations on the string worldsheet.
For AdS(3) x S(3) x S(3) x S(1) the spectrum contains heavy, as well as light
and massless modes, and we find that the one-loop contribution differs
depending on how we treat these modes showing that similar regularization
ambiguities as appeared in AdS(4)/CFT(3) occur also here.Comment: 29 pages; v2: updated references and acknowledgmen
Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a
direct superspace Feynman diagram approach, we compute the two-loop four-point
scattering amplitude with external chiral matter fields. We find that the
result is in perfect agreement with the two-loop result for a light-like
four-polygon Wilson loop. This is a nontrivial evidence of the scattering
amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR
divergent and the finite parts of our two-loop result agree with a BDS-like
ansatz for all-loop amplitudes where the scaling function is given in terms of
the N=4 SYM one, according to the conjectured Bethe equations for ABJM.
Consequently, we are able to make a prediction for the four-loop correction to
the amplitude. We also discuss the dual conformal invariance of the two-loop
result.Comment: 1+16 pages, 2 figures, minor modifications and references adde
Scattering in ABJ theories
We study the correspondence between scattering amplitudes and Wilson loops in
three-dimensional Chern-Simons matter theories. In particular, using N=2
superspace formalism, we compute at one loop the whole spectrum of four-point
superamplitudes for generic N>=2 supersymmetric theories and find a vanishing
result for N=6 ABJ(M) and N=8 BLG models. This restricts the possible range of
theories for which Wilson loops/scattering amplitudes duality might work. At
two loops, we present the computation of the four-point ABJ scattering
amplitude for external chiral superfields. Extending the known result for the
ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the
dual conformal invariance of our results and the relationship between the
Feynman diagram computation and unitarity methods. While for the ABJM theory
dual conformally invariant integrals exactly reproduce the amplitude, for the
ABJ case this happens only up to a residual constant depending on the
parity-violating parameter. Finally we propose a BDS-like exponentiation for
the amplitude based on an analogy with the four-dimensional N=4 SYM case, and
discuss its strong coupling dual counterpart.Comment: 1+54 pages, 8 figure