30 research outputs found
On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model
In this note we consider a fermionic T-duality of the coset realization of
the type IIA sigma-model on AdS_4 \times CP^3 with respect to the three flat
directions in AdS_4, six of the fermionic coordinates and three of the CP^3
directions. We show that the Buscher procedure fails as it leads to a singular
transformation and discuss the result and its implications.Comment: LaTeX2e, 9 pages, no figures, JHEP style; v2: minor clarifications;
v3: typos fixed, matches the published versio
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
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
Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons
and ABJM theory to two-loop order. For both theories we demonstrate that the
one-loop contribution to these correlators cancels. For pure Chern-Simons, we
find that specific UV divergences arise from diagrams involving two cusps,
implying the loss of finiteness and topological invariance at two-loop order.
Studying those UV divergences we derive anomalous conformal Ward identities for
n-cusped Wilson loops which restrict the finite part of the latter to
conformally invariant functions. We also compute the four-cusp Wilson loop in
ABJM theory to two-loop order and find that the result is remarkably similar to
that of the corresponding Wilson loop in N=4 SYM. Finally, we speculate about
the existence of a Wilson loop/scattering amplitude relation in ABJM theory.Comment: 37 pages, many figures; v2: references added, minor changes; v3:
references added, sign error fixed and note 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
Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
We construct a zero-curvature Lax connection in a sub-sector of the
superstring theory on AdS(4) x CP(3) which is not described by the
OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet
fermions associated to eight broken supersymmetries of the type IIA background
are physical fields. As such, the prescription for the construction of the Lax
connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4)
does not do the job. So, to construct the Lax connection we have used an
alternative method which nevertheless relies on the isometry of the target
superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde
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
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
All one-loop amplitudes in N=6 superconformal Chern-Simons theory
We exploit a recently found connection between special triple-cut diagrams
and tree-level recursive diagrams to derive a general formula capturing the
multi-particle factorisation of arbitrary one-loop amplitudes in the ABJM
theory. This formula contains certain anomalous contributions which are
reminiscent of the so-called non-factorising contributions appearing in the
factorisation of one-loop amplitudes in four-dimensional gauge theory. In the
second part of the paper we derive a recursion relation for the
supercoefficients of one-loop amplitudes in ABJM theory. By applying this
recursion relation, any one-loop supercoefficient can be reduced to special
triple-cut diagrams involving at least one four-point tree amplitude. In turn,
this implies that any one-loop supercoefficient can be derived from tree-level
recursive diagrams.Comment: 22 pages, 7 figure
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