3,578 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

### 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

### 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

### On the Integrability of large N Plane-Wave Matrix Theory

We show the three-loop integrability of large N plane-wave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory's Hamiltonian in perturbation theory and taking the large N limit. At one-loop level the result is known to be equal to the Heisenberg spin-1/2 chain, which is a well-known integrable system. Here, integrability implies the existence of hidden conserved charges and results in a degeneracy of parity pairs in the spectrum. In order to confirm integrability at higher loops, we show that this degeneracy is not lifted and that (corrected) conserved charges exist. Plane-wave matrix theory is intricately connected to N=4 Super Yang-Mills, as it arises as a consistent reduction of the gauge theory on a three-sphere. We find that after appropriately renormalizing the mass parameter of the plane-wave matrix theory the effective Hamiltonian is identical to the dilatation operator of N=4 Super Yang-Mills theory in the considered subsector. Our results therefore represent a strong support for the conjectured three-loop integrability of planar N=4 SYM and are in disagreement with a recent dual string theory finding. Finally, we study the stability of the large N integrability against nonsupersymmetric deformations of the model

### 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

### Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable
su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum
trace identities, and the spectrum for the higher-order local charges. We also
show that this method, based on operator regularization and renormalization,
which guarantees quantum integrability, as well as the construction of
self-adjoint extensions, can be used as an alternative to the discretization
procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde

### 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 $AdS_{5}\times S^{5}$, 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
$PT$ symmetric. We show that the wave functions for this system are also $PT$
symmetric. Thus, the theory is in a $PT$ 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

### On the breakdown of perturbative integrability in large N matrix models

We study the perturbative integrability of the planar sector of a massive
SU(N) matrix quantum mechanical theory with global SO(6) invariance and
Yang-Mills-like interaction. This model arises as a consistent truncation of
maximally supersymmetric Yang-Mills theory on a three-sphere to the lowest
modes of the scalar fields. In fact, our studies mimic the current
investigations concerning the integrability properties of this gauge theory.
Like in the field theory we can prove the planar integrability of the SO(6)
model at first perturbative order. At higher orders we restrict ourselves to
the widely studied SU(2) subsector spanned by two complexified scalar fields of
the theory. We show that our toy model satisfies all commonly studied
integrability requirements such as degeneracies in the spectrum, existence of
conserved charges and factorized scattering up to third perturbative order.
These are the same qualitative features as the ones found in super Yang-Mills
theory, which were enough to conjecture the all-loop integrability of that
theory. For the SO(6) model, however, we show that these properties are not
sufficient to predict higher loop integrability. In fact, we explicitly
demonstrate the breakdown of perturbative integrability at fourth order.Comment: 27 page

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