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

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

Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3

We use the algebraic curve and Luscher's mu-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) x SU(2) sector.Comment: 19 pages; v2, v3: references added, typos fixe

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

Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3

We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term L\"uscher formula based on the S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it.Comment: 21 pages, No figures, corrected typos, added some reference

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

Higher spin AdS_3 holography with extended supersymmetry

We propose a holographic duality between a higher spin AdS_3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k=N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N=3 supersymmetry of critical level model at finite k,N. In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a Z_2 automorphism truncation of a similar coset model, but at a non-critical level.Comment: 44 pages, published versio