18 research outputs found
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
Integrability and the conformal field theory of the Higgs branch
In the context of the AdS3/CFT2 correspondence, we investigate the Higgs branch CFT2. Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT2 spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS3 side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT2 side of the correspondence
Protected string spectrum in AdS(3)/CFT2 from worldsheet integrability
We derive the protected closed-string spectra of AdS3/CFT2 dual pairs with 16 supercharges at arbitrary values of the string tension and of the three-form fluxes. These follow immediately from the all-loop Bethe equations for the spectra of the integrable worldsheet theories. Further, representing the underlying integrable systems as spin chains, we find that their dynamics involves length-changing interactions and that protected states correspond to gapless excitations above the Berenstein-Maldacena-Nastase vacuum. In the case of AdS3 Ă S3 Ă T4 the degeneracies of such operators precisely match those of the dual CFT2 and the supergravity spectrum. On the other hand, we find that for AdS3 Ă S3 Ă S3 Ă S1 there are fewer protected states than previous supergravity calculations had suggested. In particular, protected states have the same su(2) charge with respect to the two three-spheres
On the massless modes of the AdS3/CFT2 integrable systems
We make a proposal for incorporating massless modes into the spin-chain of the AdS3/CFT2 integrable system. We do this by considering the α â 0 limit of the alternating d(2,1;α)2 spinchain constructed in arXiv:1106.2558. In the process we encounter integrable spin-chains with nonirreducible representations at some of their sites. We investigate their properties and construct their R-matrices in terms of Yangians
Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
We evaluate the exact one-loop partition function for fundamental strings
whose world-surface ends on a cusp at the boundary of AdS_4 and has a "jump" in
CP^3. This allows us to extract the stringy prediction for the ABJM generalized
cusp anomalous dimension Gamma_{cusp}^{ABJM} (phi,theta) up to NLO in
sigma-model perturbation theory. With a similar analysis, we present the exact
partition functions for folded closed string solutions moving in the AdS_3
parts of AdS_4 x CP^3 and AdS_3 x S^3 x S^3 x S^1 backgrounds. Results are
obtained applying to the string solutions relevant for the AdS_4/CFT_3 and
AdS_3/CFT_2 correspondence the tools previously developed for their AdS_5 x S^5
counterparts.Comment: 48 pages, 2 figures, version 3, corrected misprints in formulas 2.12,
B.86, C.33, added comment on verification of the light-like limi
Interacting finite-size magnons
We explicitly construct a large class of finite-volume two-magnon string
solutions moving on R x S^2. In particular, by making use of the relationship
between the O(3) sigma model and sine-Gordon theory we are able to find
solutions corresponding to the periodic analogues of magnon scattering and
breather-like solutions. After semi-classically quantizing these solutions we
invert the implicit expressions for the excitation energies in certain limits
and find the corrections for the multi-magnon states. For the breather-like
solutions we express the energies directly in terms of the action variable
whereas for the scattering solution we express the result as a combination of
corrections to the dispersion relation and to the scattering phase.Comment: 45pages, 7figures, v2: simplified expressions for periods and angular
momenta when elliptic modulus is greater than one, references added, typos
correcte
Integrability, spin-chains and the AdS3/CFT2 correspondence
Building on arXiv:0912.1723, in this paper we investigate the AdS3/CFT2
correspondence using integrability techniques. We present an all-loop Bethe
Ansatz (BA) for strings on AdS_3 x S^3 x S^3 x S^1, with symmetry
D(2,1;alpha)^2, valid for all values of alpha. This construction relies on a
novel, alpha-dependent generalisation of the Zhukovsky map. We investigate the
weakly-coupled limit of this BA and of the all-loop BA for strings on AdS_3 x
S^3 x T^4. We construct integrable short-range spin-chains and Hamiltonians
that correspond to these weakly-coupled BAs. The spin-chains are alternating
and homogenous, respectively. The alternating spin-chain can be regarded as
giving some of the first hints about the unknown CFT2 dual to string theory on
AdS_3 x S^3 x S^3 x S^1. We show that, in the alpha to 1 limit, the integrable
structure of the D(2,1;alpha) model is non-singular and keeps track of not just
massive but also massless modes. This provides a way of incorporating massless
modes into the integrability machinery of the AdS3/CFT2 correspondence.Comment: LaTeX, 38 pages. v2: Corrected misprints in section 6.