217 research outputs found
On the commuting charges for the highest dimension SU(2) operators in planar SYM
We consider the highest anomalous dimension operator in the SU(2) sector of
planar SYM at all-loop, though neglecting wrapping contributions.
In any case, the latter enter the loop expansion only after a precise
length-depending order. In the thermodynamic limit we write both a linear
integral equation for the Bethe root density and a linear system obeyed by the
commuting charges. Consequently, we determine the leading strong coupling
contribution to the density and from this an approximation to the leading and
sub-leading terms of any charge : it scales as , which
generalises the Gubser-Klebanov-Polyakov energy law. In the end, we briefly
extend these considerations to finite lengths and 'excited' operators by using
the idea of a non-linear integral equation.Comment: Latex file, 20 pages, some typos corrected, some technical details
expanded and explaine
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
Rational three-spin string duals and non-anomalous finite size effects
We determine by a one line computation the one-loop conformal dimension and
the associated non-anomalous finite size correction for all operators dual to
spinning strings of rational type having three angular momenta (J_1,J_2,J_3) on
S^5. Finite size corrections are conjectured to encode information about string
sigma model loop corrections to the spectrum of type IIB superstrings on
AdS_5xS^5. We compare our result to the zero-mode contribution to the leading
quantum string correction derived for the stable three-spin string with two out
of the three spin labels identical and observe agreement. As a side result we
clarify the relation between the Bethe root description of three-spin strings
of the type (J,J',J') with respectively J>J' and J<J'.Comment: 15 pages, v2: comparison to string theory changed, references added,
v3: textual modifications and title change
The Factorized S-Matrix of CFT/AdS
We argue that the recently discovered integrability in the large-N CFT/AdS
system is equivalent to diffractionless scattering of the corresponding hidden
elementary excitations. This suggests that, perhaps, the key tool for finding
the spectrum of this system is neither the gauge theory's dilatation operator
nor the string sigma model's quantum Hamiltonian, but instead the respective
factorized S-matrix. To illustrate the idea, we focus on the closed fermionic
su(1|1) sector of the N=4 gauge theory. We introduce a new technique, the
perturbative asymptotic Bethe ansatz, and use it to extract this sector's
three-loop S-matrix from Beisert's involved algebraic work on the three-loop
su(2|3) sector. We then show that the current knowledge about semiclassical and
near-plane-wave quantum strings in the su(2), su(1|1) and sl(2) sectors of
AdS_5 x S^5 is fully consistent with the existence of a factorized S-matrix.
Analyzing the available information, we find an intriguing relation between the
three associated S-matrices. Assuming that the relation also holds in gauge
theory, we derive the three-loop S-matrix of the sl(2) sector even though this
sector's dilatation operator is not yet known beyond one loop. The resulting
Bethe ansatz reproduces the three-loop anomalous dimensions of twist-two
operators recently conjectured by Kotikov, Lipatov, Onishchenko and Velizhanin,
whose work is based on a highly complex QCD computation of Moch, Vermaseren and
Vogt.Comment: 38 pages, LaTeX, JHEP3.cl
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
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
The SU(3) spin chain sigma model and string theory
The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous
dimension of single trace operators involving the three complex scalars of N=4
supersymmetric Yang-Mills. We construct the non-linear sigma model describing
the continuum limit of the SU(3) spin chain. We find that this sigma model
corresponds to a string moving with large angular momentum in the five-sphere
in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular
strings with angular momenta along three orthogonal directions of the
five-sphere is reproduced as a particular case from the spin chain sigma model.Comment: 14 pages. Latex.v2: Misprints corrected. v3: Minor changes and
improved details from journal versio
Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
It was recently shown that the string theory duals of certain deformations of
the N=4 gauge theory can be obtained by a combination of T-duality
transformations and coordinate shifts. Here we work out the corresponding
procedure of twisting the dual integrable spin chain and its Bethe ansatz. We
derive the Bethe equations for the complete twisted N=4 gauge theory at one and
higher loops. These have a natural generalization which we identify as twists
involving the Cartan generators of the conformal algebra. The underlying model
appears to be a form of noncommutative deformation of N=4 SYM.Comment: 28 pages, v2: reference flip corrected, v3: some typos in
(4.10,4.20,5.5) correcte
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
Planar N=4 Gauge Theory and the Hubbard Model
Recently it was established that a certain integrable long-range spin chain
describes the dilatation operator of N=4 gauge theory in the su(2) sector to at
least three-loop order, while exhibiting BMN scaling to all orders in
perturbation theory. Here we identify this spin chain as an approximation to an
integrable short-ranged model of strongly correlated electrons: The Hubbard
model.Comment: 35 pages, 2 figures; v2: typos and references fixed, published
versio
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