668 research outputs found
Magnon dispersion to four loops in the ABJM and ABJ models
The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry
which is believed to be integrable in the planar limit. However, there is a
coupling dependent function that appears in the magnon dispersion relation and
the asymptotic Bethe ansatz that is only known to leading order at strong and
weak coupling. We compute this function to four loops in perturbation theory by
an explicit Feynman diagram calculation for both the ABJM model and the ABJ
extension. We find that all coefficients have maximal transcendentality. We
then compute the four-loop wrapping correction for a scalar operator in the 20
of SU(4) and find that it agrees with a recent prediction from the ABJM
Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ
model that might be perturbatively integrable at all loop orders but has a
short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram
corrected: modified result in the ABJ case only, formulations improved, typos
fixed, references added; v3: signs of three diagrams corrected, modifying the
final resul
Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
This paper studies giant magnons in AdS_4 x CP^3 using both the string
sigma-model and the algebraic curve. We complete the dictionary of solutions by
finding the dyonic generalisation of the CP^1 string solution, which matches
the `small' giant magnon in the algebraic curve, and by pointing out that the
solution recently constructed by the dressing method is the `big' giant magnon.
We then use the curve to compute finite-J corrections to all cases, which for
the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we
recover the S^5 answer, but for the `small' and `big' giant magnons we obtain
new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and
minor clarification
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On the singularities of the R-R AdS(3) x S-3 x T-4 S matrix
We investigate the analytic properties of the exact magnon Smatrix of stringtheory on AdS3×S3×T4with R-R flux. We show that the previously proposeddressing factors have the exact double-pole/zero structure expected from Landaubox diagrams. This constitutes a strong consistency check of our dressing factors,much as the Dorey-Hofman-Maldacena poles do for the all-loop dressing factor inAdS5×S5
Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
Using N=2 superspace techniques we compute the four-loop spectrum of single
trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric
Chern-Simons theories. Our computation yields a four-loop contribution to the
function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion
relation which has fixed maximum transcendentality and coincides with the
findings in components given in the revised versions of arXiv:0908.2463 and
arXiv:0912.3460. We also discuss possible scenarios for an all-loop function
h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved,
references adde
Free field realization of the exceptional current superalgebra \hat{D(2,1;\a)}_k
The free-field representations of the D(2,1;\a) current superalgebra and
the corresponding energy-momentum tensor are constructed. The related screening
currents of the first kind are also presented.Comment: Latex file, 10 page
Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of
Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct
a set of finite-gap equations that describe the classical string spectrum.
Using the recently proposed all-loop S-matrix we write down the all-loop Bethe
ansatz equations for the massive sector. In the thermodynamic limit the Bethe
ansatz reproduces the finite-gap equations. As part of this derivation we
propose expressions for the leading order dressing phases. These phases differ
from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure
Ramond-Ramond case. We also consider the one-loop quantization of the algebraic
curve and determine the one-loop corrections to the dressing phases. Finally we
consider some classical string solutions including finite size giant magnons
and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about
perturbative results adde
The low-energy limit of AdS(3)/CFT2 and its TBA
We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states
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