460 research outputs found
On the Scattering Phase for AdS_5 x S^5 Strings
We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x
S^5 apparently solving Janik's crossing relation.Comment: 9 pages, v2: revised conclusions about agreement with perturbative
string theory; minor changes, v3: resolution to above problems indicated, to
appear in Mod. Phys. Lett.
On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
We consider the highest-energy state in the su(1|1) sector of N=4 super
Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z
is a complex scalar and \psi is a component of gaugino. We show that this state
corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the
antiferromagnetic state in the su(2) sector. We find perturbative expansions of
the energy of this state in both weak and strong 't Hooft coupling regimes
using asymptotic gauge theory Bethe ansatz equations. We also discuss a
possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late
Integrability and Transcendentality
We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of
N=4 gauge theory directly from the field theory. We then analyze a recently
proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large
spacetime spin at large but finite twist, and find a novel all-loop scaling
function. This function obeys the Kotikov-Lipatov transcendentality principle
and does not depend on the twist. Under the assumption that one may extrapolate
back to leading twist, our result yields an all-loop prediction for the
large-spin anomalous dimensions of twist-two operators. The latter also appears
as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov
for the all-loop structure of the maximally helicity violating (MHV) n-point
gluon amplitudes of N=4 gauge theory. This potentially establishes a direct
link between the worldsheet and the spacetime S-matrix approach. A further
assumption for the validity of our prediction is that perturbative BMN
(Berenstein-Maldacena-Nastase) scaling does not break down at four loops, or
beyond. We also discuss how the result gets modified if BMN scaling does break
down. Finally, we show that our result qualitatively agrees at strong coupling
with a prediction of string theory.Comment: 45 pages LaTeX, 3 postscript figures. v2: Chapter on BMN scaling and
transcendentality added. v3: version accepted for publication in JSTA
A Generalized Scaling Function for AdS/CFT
We study a refined large spin limit for twist operators in the sl(2) sector
of AdS/CFT. We derive a novel non-perturbative equation for the generalized
two-parameter scaling function associated to this limit, and analyze it at weak
coupling. It is expected to smoothly interpolate between weakly coupled gauge
theory and string theory at strong coupling.Comment: 27 pages, no figures; v2: references added and typos fixe
Matching Higher Conserved Charges for Strings and Spins
We demonstrate that the recently found agreement between one-loop scaling
dimensions of large dimension operators in N=4 gauge theory and energies of
spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite
number of hidden higher commuting charges. This dynamical agreement is of a
mathematically highly intricate and non-trivial nature. In particular, on the
gauge side the generating function for the commuting charges is obtained by
integrable quantum spin chain techniques from the thermodynamic density
distribution function of Bethe roots. On the string side the generating
function, containing information to arbitrary loop order, is constructed by
solving exactly the Backlund equations of the integrable classical string sigma
model. Our finding should be an important step towards matching the integrable
structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof
that the entire infinite towers of commuting gauge and string charges match);
references adde
Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
The super Yang-Mills duals of open strings attached to maximal giant
gravitons are studied in perturbation theory. It is shown that non-BPS baryonic
excitations of the gauge theory can be studied within the paradigm of open
quantum spin chains even beyond the leading order in perturbation theory. The
open spin chain describing the two loop mixing of non-BPS giant gravitons
charged under an su(2) of the so(6) R symmetry group is explicitly constructed.
It is also shown that although the corresponding open spin chain is integrable
at the one loop order, there is a potential breakdown of integrability at two
and higher loops. The study of integrability is performed using coordinate
Bethe ansatz techniques.Comment: 28 pages. References added in revised versio
Quantum corrections to the string Bethe ansatz
One-loop corrections to the energy of semiclassical rotating strings contain
both analytic and non-analytic terms in the 't Hooft coupling. Analytic
contributions agree with the prediction from the string Bethe ansatz based on
the classical S-matrix, but in order to include non-analytic contributions
quantum corrections are required. We find a general expression for the first
quantum correction to the string Bethe ansatz.Comment: 12 pages. Latex. v2: Misprints corrected and references adde
New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
We consider classical superstrings propagating on AdS_5 x S^5 space-time. We
consistently truncate the superstring equations of motion to the so-called
su(1|1) sector. By fixing the uniform gauge we show that physical excitations
in this sector are described by two complex fermionic degrees of freedom and we
obtain the corresponding Lagrangian. Remarkably, this Lagrangian can be cast in
a two-dimensional Lorentz-invariant form. The kinetic part of the Lagrangian
induces a non-trivial Poisson structure while the Hamiltonian is just the one
of the massive Dirac fermion. We find a change of variables which brings the
Poisson structure to the canonical form but makes the Hamiltonian nontrivial.
The Hamiltonian is derived as an exact function of two parameters: the total
S^5 angular momentum J and string tension \lambda; it is a polynomial in 1/J
and in \sqrt{\lambda'} where \lambda'=\frac{\lambda}{J^2} is the effective BMN
coupling. We identify the string states dual to the gauge theory operators from
the closed su(1|1) sector of N=4 SYM and show that the corresponding near-plane
wave energy shift computed from our Hamiltonian perfectly agrees with that
recently found in the literature. Finally we show that the Hamiltonian is
integrable by explicitly constructing the corresponding Lax representation.Comment: 35 pages;v2:typos corrected, references adde
Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
We propose a perturbative asymptotic Bethe ansatz (PABA) for open spin-chain
systems whose Hamiltonians are given by matrices of anomalous dimension for
composite operators, and apply it to two types of composite operators related
to two different brane configurations. One is an AdS_4 \times S^2-brane in the
bulk AdS_5 \times S^5 which gives rise to a defect conformal field theory
(dCFT) in the dual field theory, and the other is a giant graviton system with
an open string excitation. In both cases, excitations on open strings attaching
to D-branes (a D5-brane for the dCFT case, and a spherical D3-brane for the
giant graviton case) can be represented by magnon states in the spin-chains
with appropriate boundary conditions, in which informations of the D-branes are
encoded. We concentrate on single-magnon problems, and explain how to calculate
boundary S-matrices via the PABA technique. We also discuss the energy spectrum
in the BMN limit.Comment: 1+24 pages, 1 figure, typos corrected, references added, discussions
on the integrability for giant gravitons modified, version to appear in JHE
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