1,014 research outputs found
Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
We study the supersymmetry generators Q, S on the 1-loop vectorless sector of
N=4 Super Yang-Mills, by reduction to the plane-wave matrix model. Using a
coherent basis in the su(2|2) sector, a comparison with the algebra given by
Beisert in nlin/0610017 is presented, and some parameters (up to one-loop) are
determined. We make a final comparison of these supercharges with the results
that can be obtained from the string action by working in the light-cone-gauge
and discretizing the string.Comment: 20 pages, no figures v2: Typos corrected, references adde
Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
In this contribution we briefly review recent developments in the theory of
long-range integrable spin chains. These spin chains constitute a natural
generalisation of the well-studied integrable nearest-neighbour chains and are
of particular relevance to the integrability in the AdS/CFT correspondence
since the dilatation operator in the asymptotic region is conjectured to be a
Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3: minor typos corrected, references adde
The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD
We evaluate the full planar one-loop dilation operator of N=2 SuperConformal
QCD, the SU(N_c) super Yang-Mills theory with N_f = 2 N_c fundamental
hypermultiplets, in the flavor-singlet sector. Remarkably, the spin-chain
Hamiltonian turns out to be completely fixed by superconformal symmetry, as in
N=4 SYM. We present a more general calculation, for the superconformal quiver
theory with SU(N_c)X SU(N_c) gauge group, which interpolates between N=2 SCQCD
and the Z_2 orbifold of N=4 SYM; here symmetry fixes the Hamiltonian up to a
single parameter, corresponding to the ratio of the two marginal gauge
couplings.Comment: v2: typo corrected, cosmetic changes. JHEP versio
Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
We consider twist-3 operators in the sl(2) sector of N=4 SYM built out of
three scalar fields with derivatives. We extract from the Bethe Ansatz
equations of this sector the exact lowest anomalous dimension gamma(s) of
scaling fields for several values of the operator spin s. We propose compact
closed expressions for the spin dependence of gamma(s) up to the four loop
level and show that they obey a simple new twist-3 transcendentality principle.
As a check, we reproduce the four loop universal cusp anomalous dimension
governing the logarithmic large spin limit of gamma(s).Comment: 26 pages, JHEP styl
The Ising model and planar N=4 Yang-Mills
The scattering-matrix for planar Yang-Mills with N=4 supersymmetry relies on
the assumption that integrability holds to all orders in perturbation theory.
In this note we define a map from the spectral variables x^{\pm},
parameterizing the long-range magnon momenta, to couplings in a two-dimensional
Ising model. Under this map integrability of planar N=4 Yang-Mills becomes
equivalent to the Yang-Baxter equation for the two-dimensional Ising model, and
the long-range variables x^{\pm} translate into the entries of the Ising
transfer matrices. We explore the Ising correlation length which equals the
inverse magnon momentum in the small momentum limit. The critical regime is
thus reached for vanishing magnon momentum. We also discuss the meaning of the
Kramers-Wannier duality transformation on the gauge theory, together with that
of the Ising model critical points.Comment: 24 pages. v2: References added and minor typos correcte
Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
We define Landau-Lifshitz sigma models on general coset space , with
a maximal stability sub-group of . These are non-relativistic models that
have -valued N\"other charges, local invariance and are classically
integrable. Using this definition, we construct the
Landau-Lifshitz sigma-model. This sigma model describes the thermodynamic limit
of the spin-chain Hamiltonian obtained from the complete one-loop dilatation
operator of the N=4 super Yang-Mills (SYM) theory. In the second part of the
paper, we identify a number of consistent truncations of the Type IIB
Green-Schwarz action on whose field content consists of two
real bosons and 4,8 or 16 real fermions. We show that -symmetry acts
trivially in these sub-sectors. In the context of the large spin limit of the
AdS/CFT correspondence, we map the Lagrangians of these sub-sectors to
corresponding truncations of the Landau-Lifshitz
sigma-model.Comment: 42 page
Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
We study issues concerning perturbative integrability of N=6 Chern-Simons
theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics,
we derive so called maximal-ranged interactions in the quantum dilatation
generator, originating from homogeneous and inhomogeneous diagrams. These
diagrams require proper regularization of not only ultraviolet but also
infrared divergences. We first consider standard operator mixing method. We
show that homogeneous diagrams are obtainable by recursive method to all
orders. The method, however, is not easily extendable to inhomogeneous
diagrams. We thus consider two-point function method and study both operator
contents and spectrum of the quantum dilatation generator up to six loop
orders. We show that, of two possible classes of operators, only one linear
combination actually contributes. Curiously, this is exactly the same
combination as in N=4 super Yang-Mills theory. We then study spectrum of
anomalous dimension up to six loops. We find that the spectrum agrees perfectly
with the prediction based on quantum integrability. In evaluating the six loop
diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by
Ferguson, Baily and Arno.Comment: 1+39 pages, 12 figures, references added, minor structural changes,
typos correcte
The Bethe Ansatz for AdS5 x S5 Bound States
We reformulate the nested coordinate Bethe ansatz in terms of coproducts of
Yangian symmetry generators. This allows us to derive the nested Bethe
equations for the bound state string S-matrices. We find that they coincide
with the Bethe equations obtained from a fusion procedure. The bound state
number dependence in the Bethe equations appears through the parameters x^{\pm}
and the dressing phase only.Comment: typos correcte
The Bound State S-Matrix for AdS5 x S5 Superstring
We determine the S-matrix that describes scattering of arbitrary bound states
in the light-cone string theory in AdS5 x S5. The corresponding construction
relies on the Yangian symmetry and the superspace formalism for the bound state
representations. The basic analytic structure supporting the S-matrix entries
turns out to be the hypergeometric function 4F3. We show that for particular
bound state numbers it reproduces all the scattering matrices previously
obtained in the literature. Our findings should be relevant for the TBA and
Luescher approaches to the finite-size spectral problem. They also shed some
light on the construction of the universal R-matrix for the centrally-extended
psu(2|2) superalgebra.Comment: 37 pages, 2 figures, v2: typos correcte
Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
We propose a closed expression for the three loop anomalous dimension of a
class of twist-3 operators built with gauge fields and covariant derivatives.
To this aim, we solve the long-range Bethe Ansatz equations at finite spin and
provide a consistent analytical formula obtained assuming maximal
transcendentality violation as suggested by the known one-loop anomalous
dimension. The final result reproduces the universal cusp anomalous dimension
and obeys recursion relations inspired by the principle of reciprocity
invariance.Comment: 20 pages, JHEP styl
- …