23 research outputs found
Superconformal operators in Yang-Mills theories on the light-cone
We employ the light-cone superspace formalism to develop an efficient
approach to constructing superconformal operators of twist two in Yang-Mills
theories with N=1,2,4 supercharges. These operators have an autonomous scale
dependence to one-loop order and determine the eigenfunctions of the dilatation
operator in the underlying gauge theory. We demonstrate that for arbitrary N
the superconformal operators are given by remarkably simple, universal
expressions involving the light-cone superfields. When written in components
field, they coincide with the known results obtained by conventional
techniques.Comment: 29 pages, Late
Classical/quantum integrability in AdS/CFT
We discuss the AdS/CFT duality from the perspective of integrable systems and
establish a direct relationship between the dimension of single trace local
operators composed of two types of scalar fields in N=4 super Yang-Mills and
the energy of their dual semiclassical string states in AdS(5) X S(5). The
anomalous dimensions can be computed using a set of Bethe equations, which for
``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified
approach to the long wavelength Bethe equations, the classical ferromagnet and
the classical string solutions in the SU(2) sector and present a general
solution, governed by complex curves endowed with meromorphic differentials
with integer periods. Using this solution we compute the anomalous dimensions
of these long operators up to two loops and demonstrate that they agree with
string-theory predictions.Comment: 49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop
equivalence between the sigma model and the gauge theory is added. References
added; v4,v5,v6: misprints correcte
Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling
behavior in the limit when their Lorentz spin grows exponentially with the
twist. To describe the corresponding scaling function in planar N=4 SYM theory,
we analyze an integral equation recently proposed by Freyhult, Rej and
Staudacher and argue that at strong coupling it can be casted into a form
identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6)
sigma model. This result is in a perfect agreement with the proposal put
forward by Alday and Maldacena within the dual string description, that the
scaling function should coincide with the energy density of the nonlinear O(6)
sigma model embedded into AdS_5xS^5.Comment: 25 page
Superconformal operators in N=4 super-Yang-Mills theory
We construct, in the framework of the N=4 SYM theory, a supermultiplet of
twist-two conformal operators and study their renormalization properties. The
components of the supermultiplet have the same anomalous dimension and enter as
building blocks into multi-particle quasipartonic operators. The latter are
determined by the condition that their twist equals the number of elementary
constituent fields from which they are built. A unique feature of the N=4 SYM
is that all quasipartonic operators with different SU(4) quantum numbers fall
into a single supermultiplet. Among them there is a subsector of the operators
of maximal helicity, which has been known to be integrable in the multi-color
limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM
theory, this symmetry is extended to the whole supermultiplet of quasipartonic
operators and the one-loop dilatation operator coincides with a Hamiltonian of
integrable SL(2|4) Heisenberg spin chain.Comment: 45 pages, Latex, 4 figure
Nonforward anomalous dimensions of Wilson operators in N=4 super-Yang-Mills theory
We present the next-to-leading order results for universal non-forward
anomalous dimensions of Wilson twist-2 operators in N=4 supersymmetric
Yang-Mills theory. The whole calculation was performed using supersymmetric
Ward identities derived in this paper together with already known QCD results
and does not involve any additional calculation of diagrams. We also considered
one particular limit of our result, which could potentially be interesting in
the context of AdS/CFT correspondence.Comment: 15 pages, references added, typos corrected, version accepted in JHE
Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
Anomalous dimensions of high-twist Wilson operators in generic gauge theories
occupy a band of width growing logarithmically with their conformal spin. We
perform a systematic study of its fine structure in the autonomous SL(2)
subsector of the dilatation operator of planar N=4 super Yang-Mills theory
which is believed to be integrable to all orders in 't Hooft coupling. We
resort in our study on the framework of the Baxter equation to unravel the
properties of the ground state trajectory and the excited trajectories in the
spectrum. We use two complimentary approaches in our analysis based on the
asymptotic solution of the Baxter equation and on the semiclassical expansion
to work out the leading asymptotic expression for the trajectories in the upper
and lower part of the band and to find how they are modified by the
perturbative corrections.Comment: 34 pages; v2: minor corrections, reference adde
Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
We review the construction of the AdS/CFT dressing factor, its analytic
properties and several checks of its validity.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters update