162 research outputs found
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
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
Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theory
We study rotating strings with multiple spins in the background of
, which is dual to a superconformal field
theory with global symmetry via the AdS/CFT
correspondence. We analyse the limiting behaviour of macroscopic strings and
discuss the identification of the dual operators and how their anomalous
dimensions should behave as the global charges vary. A class of string
solutions we find are dual to operators in SU(2) subsector, and our result
implies that the one-loop planar dilatation operator restricted to the SU(2)
subsector should be equivalent to the hamiltonian of the integrable Heisenberg
spin chain.Comment: 8 pages, revtex4, twocolum
UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
We consider the Pohlmeyer-type reduced theory found by explicitly solving the
Virasoro constraints in the formulation of AdS_5xS^5 superstring in terms of
supercoset currents. The resulting set of classically equivalent, integrable
Lagrangian equations of motion has the advantage of involving only a physical
number of degrees of freedom and yet being 2d Lorentz invariant. The
corresponding reduced theory action may be written as a gauged WZW model
coupled to fermions with further bosonic and fermionic potential terms. Since
the AdS_5xS^5 superstring sigma model is conformally invariant, its classical
relation to the reduced theory may extend to the quantum level only if the
latter is, in fact, UV finite. This theory is power counting renormalizable
with the only possible divergences being of potential type. We explicitly
verify its 1-loop finiteness and show that the 2-loop divergences are, in
general, scheme dependent and vanish in dimensional reduction scheme. We expect
that the reduced theory is finite to all orders in the loop expansion.Comment: 40 pages, Latex; v2: typos corrected, minor clarifying remarks adde
Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
We investigate the structure of the quantum S-matrix for perturbative
excitations of the Pohlmeyer reduced version of the AdS_5 x S^5 superstring
following arXiv:0912.2958. The reduced theory is a fermionic extension of a
gauged WZW model with an integrable potential. We use as an input the result of
the one-loop perturbative scattering amplitude computation and an analogy with
simpler reduced AdS_n x S^n theories with n=2,3. The n=2 theory is equivalent
to the N=2 2-d supersymmetric sine-Gordon model for which the exact quantum
S-matrix is known. In the n=3 case the one-loop perturbative S-matrix, improved
by a contribution of a local counterterm, satisfies the group factorization
property and the Yang-Baxter equation, and reveals the existence of a novel
quantum-deformed 2-d supersymmetry which is not manifest in the action. The
one-loop perturbative S-matrix of the reduced AdS_5 x S^5 theory has the group
factorisation property but does not satisfy the Yang-Baxter equation suggesting
some subtlety with the realisation of quantum integrability. As a possible
resolution, we propose that the S-matrix of this theory may be identified with
the quantum-deformed [psu(2|2)]^2 x R^2 symmetric R-matrix constructed in
arXiv:1002.1097. We conjecture the exact all-order form of this S-matrix and
discuss its possible relation to the perturbative S-matrix defined by the path
integral. As in the AdS_3 x S^3 case the symmetry of the S-matrix may be
interpreted as an extended quantum-deformed 2-d supersymmetry.Comment: 61 pages, 2 figures; v2: minor corrections and reference added; v3:
minor correction
Conformal SO(2,4) Transformations for the Helical AdS String Solution
By applying the conformal SO(2,4) transformations to the folded rotating
string configuration with two spins given by a certain limit from the helical
string solution in AdS_3 x S^1, we construct new string solutions whose
energy-spin relations are characterized by the boost parameter. When two
SO(2,4) transformations are performed with two boost parameters suitably
chosen, the straight folded rotating string solution with one spin in AdS_3 is
transformed in the long string limit into the long spiky string solution whose
expression is given from the helical string solution in AdS_3 by making a limit
that the modulus parameter becomes unity.Comment: 16 pages, LaTex, no figure
An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel
symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue
the origin of this symmetry in the exceptional superalgebra d(2,1;epsilon),
which recovers su(2|2) when the parameter epsilon is taken to zero. Especially,
we rederive the Yangian symmetries of the AdS/CFT spin chain using the
exceptional superalgebra and find that the epsilon-correction corresponds to
the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of
the AdS/CFT spin chain expressed with this symmetry from the canonical one of
the exceptional algebra.Comment: 20 pages, 3 figures, v3: minor changes and references adde
Stringing Spins and Spinning Strings
We apply recently developed integrable spin chain and dilatation operator
techniques in order to compute the planar one-loop anomalous dimensions for
certain operators containing a large number of scalar fields in N =4 Super
Yang-Mills. The first set of operators, belonging to the SO(6) representations
[J,L-2J,J], interpolate smoothly between the BMN case of two impurities (J=2)
and the extreme case where the number of impurities equals half the total
number of fields (J=L/2). The result for this particular [J,0,J] operator is
smaller than the anomalous dimension derived by Frolov and Tseytlin
[hep-th/0304255] for a semiclassical string configuration which is the dual of
a gauge invariant operator in the same representation. We then identify a
second set of operators which also belong to [J,L-2J,J] representations, but
which do not have a BMN limit. In this case the anomalous dimension of the
[J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that
the fluctuation spectra for this [J,0,J] operator is consistent with the string
prediction.Comment: 27 pages, 4 figures, LaTex; v2 reference added, typos fixe
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
The polarization evolution of the optical afterglow of GRB 030329
We report 31 polarimetric observations of the afterglow of GRB 030329 with
high signal-to-noise and high sampling frequency. The data imply that the
afterglow magnetic field has small coherence length and is mostly random,
probably generated by turbulence.Comment: 2003 GRB Conference, Santa Fe, Oct. 2003, 1 ps-figur
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