34 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
Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
We compute the first curvature corrections to the spectrum of light-cone
gauge type IIA string theory that arise in the expansion of about a plane-wave limit. The resulting spectrum is shown to
match precisely, both in magnitude and degeneration that of the corresponding
solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion
relation correction is calculated for all the single oscillator states of the
theory, with the level matching condition lifted. It is shown to have all
logarithmic divergences cancelled and to leave only a finite exponentially
suppressed contribution, as shown earlier for light bosons. We argue that there
is no ambiguity in the choice of the regularization for the self-energy sum,
since the regularization applied is the only one preserving unitarity.
Interaction matrices in the full degenerate two-oscillator sector are
calculated and the spectrum of all two light magnon oscillators is completely
determined. The same finite-size corrections, at the order 1/J, where is
the length of the chain, in the two-magnon sector are calculated from the all
loop Bethe Ansatz. The corrections obtained by the two completely different
methods coincide up to the fourth order in . We
conjecture that the equivalence extends to all orders in and to
higher orders in 1/J.Comment: 32 pages. Published version; journal reference 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
On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
We perform a detailed study of the type IIA superstring in AdS(4) x CP(3).
After introducing suitable bosonic light-cone and fermionic kappa worldsheet
gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone
Hamiltonian up to quartic order in fields.
As a first application of our derivation we calculate energy shifts for
string configurations in a closed fermionic subsector and successfully match
these with a set of light-cone Bethe equations. We then turn to investigate the
mismatch between the degrees of freedom of scattering states and oscillatory
string modes. Since only light string modes appear as fundamental Bethe roots
in the scattering theory, the physical role of the remaining massive
oscillators is rather unclear. By continuing a line of research initiated by
Zarembo, we shed light on this question by calculating quantum corrections for
the propagators of the bosonic massive fields. We show that, once loop
corrections are incorporated, the massive coordinates dissolve in a continuum
state of two light particles.Comment: 40 pages, 2 figures. v3: Minor clarifications made and reference list
updated. Published version
Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
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.Comment: 28 pages; v2: Fixed signs and eq. (B.1), results unchanged, one
reference added; v3: Matches published versio
One Loop Amplitudes In ABJM
For three dimensional N=6 superconformal field theories we compute one-loop
scattering amplitudes for any number of external particles. We focus on a
particular subsector of N=2 invariant superamplitudes for which the ordinary
perturbative evaluation becomes very easy. The result we obtain is in general
non-vanishing. For six external particles our findings are sufficient for
determining the complete expression of the N=6 superamplitude at this order. We
discuss the symmetries of the result and its anomalous variation under
superconformal generators.Comment: 1+34 pages, 4 figures, references added, published versio
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