3,026 research outputs found
Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
Quantum spin chains arise naturally from perturbative large-N field theories
and matrix models. The Hamiltonian of such a model is a long-range deformation
of nearest-neighbor type interactions. Here, we study the most general
long-range integrable spin chain with spins transforming in the fundamental
representation of gl(n). We derive the Hamiltonian and the corresponding
asymptotic Bethe ansatz at the leading four perturbative orders with several
free parameters. Furthermore, we propose Bethe equations for all orders and
identify the moduli of the integrable system. We finally apply our results to
plane-wave matrix theory and show that the Hamiltonian in a closed sector is
not of this form and therefore not integrable beyond the first perturbative
order. This also implies that the complete model is not integrable.Comment: 22 pages, v2: reference adde
World-sheet scattering in AdS_5 x S^5 at two loops
We study the AdS_5 x S^5 sigma-model truncated to the near-flat-space limit
to two-loops in perturbation theory. In addition to extending previously known
one-loop results to the full SU(2|2)^2 S-matrix we calculate the two-loop
correction to the dispersion relation and then compute the complete two-loop
S-matrix. The result of the perturbative calculation can be compared with the
appropriate limit of the conjectured S-matrix for the full theory and complete
agreement is found.Comment: 26pages, 3 figure
The prompt optical/near-infrared flare of GRB 050904: the most luminous transient ever detected
With a redshift of z=6.295, GRB 050904 is the most distant gamma-ray burst
ever discovered. It was an energetic event at all wavelengths and the afterglow
was observed in detail in the near-infrared bands. We gathered all available
optical and NIR afterglow photometry of this GRB to construct a composite NIR
light curve spanning several decades in time and flux density. Transforming the
NIR light curve into the optical, we find that the afterglow of GRB 050904 was
more luminous at early times than any other GRB afterglow in the
pre-\emph{Swift} era, making it at these wavelengths the most luminous
transient ever detected. Given the intrinsic properties of GRB 050904 and its
afterglow, we discuss if this burst is markedly different from other GRBs at
lower redshifts.Comment: The Astronomical Journal, in press; revised version, including the
comments of the referee (one figure added, text restructured, all conclusions
unchanged), 7 pages, 3 figure
Magnon Bound-state Scattering in Gauge and String Theory
It has been shown that, in the infinite length limit, the magnons of the
gauge theory spin chain can form bound states carrying one finite and one
strictly infinite R-charge. These bound states have been argued to be
associated to simple poles of the multi-particle scattering matrix and to world
sheet solitons carrying the same charges. Classically, they can be mapped to
the solitons of the complex sine-Gordon theory.
Under relatively general assumptions we derive the condition that simple
poles of the two-particle scattering matrix correspond to physical bound states
and construct higher bound states ``one magnon at a time''. We construct the
scattering matrix of the bound states of the BDS and the AFS S-matrices. The
bound state S-matrix exhibits simple and double poles and thus its analytic
structure is much richer than that of the elementary magnon S-matrix. We also
discuss the bound states appearing in larger sectors and their S-matrices. The
large 't Hooft coupling limit of the scattering phase of the bound states in
the SU(2) sector is found to agree with the semiclassical scattering of world
sheet solitons. Intriguingly, the contribution of the dressing phase has an
independent world sheet interpretation as the soliton-antisoliton scattering
phase shift. The small momentum limit provides independent tests of these
identifications.Comment: 25 pages, Latex V2: clarifying comments added to footnote 1 and
footnote 10; references added V3: typos correcte
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
Worldsheet Form Factors in AdS/CFT
We formulate a set of consistency conditions appropriate to worldsheet form
factors in the massive, integrable but non-relativistic, light-cone gauge fixed
AdS(5) x S**5 string theory. We then perturbatively verify that these
conditions hold, at tree level in the near-plane-wave limit and to one loop in
the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We
further study the form factors in the weakly coupled dual description,
verifying that the relevant conditions naturally hold for the one-loop
Heisenberg spin-chain. Finally, we note that the near-plane-wave expressions
for the form factors, when further expanded in small momentum or, equivalently,
large charge density, reproduce the thermodynamic limit of the spin-chain
results at leading order.Comment: 30 pages, 12 figures, v3: typos fixed, improved discussion of bound
states and bound state axio
The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
We study the question of diagonalizability of the Hamiltonian for the
Faddeev-Reshetikhin (FR) model in the two particle sector. Although the two
particle S-matrix element for the FR model, which may be relevant for the
quantization of strings on , has been calculated recently
using field theoretic methods, we find that the Hamiltonian for the system in
this sector is not diagonalizable. We trace the difficulty to the fact that the
interaction term in the Hamiltonian violating Lorentz invariance leads to
discontinuity conditions (matching conditions) that cannot be satisfied. We
determine the most general quartic interaction Hamiltonian that can be
diagonalized. This includes the bosonic Thirring model as well as the bosonic
chiral Gross-Neveu model which we find share the same S-matrix. We explain this
by showing, through a Fierz transformation, that these two models are in fact
equivalent. In addition, we find a general quartic interaction Hamiltonian,
violating Lorentz invariance, that can be diagonalized with the same two
particle S-matrix element as calculated by Klose and Zarembo for the FR model.
This family of generalized interaction Hamiltonians is not Hermitian, but is
symmetric. We show that the wave functions for this system are also
symmetric. Thus, the theory is in a unbroken phase which guarantees the
reality of the energy spectrum as well as the unitarity of the S-matrix.Comment: 32 pages, 1 figure; references added, version published in JHE
Near-flat space limit and Einstein manifolds
We study the near-flat space limit for strings on AdS(5)xM(5), where the
internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1)
isometry. In the bosonic sector, the limiting sigma model is similar to the one
found for AdS(5)xS(5), as the global symmetries are reduced in the most general
case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r),
whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the
same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates
the generic presence of integrable subsectors in AdS/CFT.Comment: 30 pages, 1 figur
Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes
We compute one-loop S-matrix in the reduced sigma-model which describes AdS_5
x S^5 string theory in the near-flat-space limit. The result agrees with the
corresponding limit of the S-matrix in the full sigma-model, which demonstrates
the consistency of the reduction at the quantum level.Comment: 9 pages, 1 figure; v2: reference added; v3: misprint in (3.6)
corrected; v4: typo in (3.4) corrected; v5: new form of the actio
Classical r-matrix of the su(2|2) SYM spin-chain
In this note we straightforwardly derive and make use of the quantum R-matrix
for the su(2|2) SYM spin-chain in the manifest su(1|2)-invariant formulation,
which solves the standard quantum Yang-Baxter equation, in order to obtain the
correspondent (undressed) classical r-matrix from the first order expansion in
the ``deformation'' parameter 2 \pi / \sqrt{\lambda}, and check that this last
solves the standard classical Yang-Baxter equation. We analyze its bialgebra
structure, its dependence on the spectral parameters and its pole structure. We
notice that it still preserves an su(1|2) subalgebra, thereby admitting an
expression in terms of a combination of projectors, which spans only a subspace
of su(1|2) \otimes su(1|2). We study the residue at its simple pole at the
origin, and comment on the applicability of the classical Belavin-Drinfeld type
of analysis.Comment: 14 pages, LaTeX, no figures; corrections made, further analysis of
the residue and references adde
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