216 research outputs found
The Bajnok-Janik formula and wrapping corrections
We write down the simplified TBA equations of the string
sigma-model for minimal energy twist-two operators in the sl(2) sector of the
model. By using the linearized version of these TBA equations it is shown that
the wrapping corrected Bethe equations for these states are identical, up to
O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach
(Bajnok-Janik formula). Applications of the Bajnok-Janik formula to
relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and
the SU(n) principal sigma models, are also discussed.Comment: Latex, 22 pages, published versio
Lifting asymptotic degeneracies with the Mirror TBA
We describe a qualitative feature of the AdS_5 x S^5 string spectrum which is
not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced
discrete symmetry in the asymptotic limit, whereby extra energy degeneracy
enters the spectrum. We discuss how finite size corrections should lift this
degeneracy, through both perturbative (Luscher) and non-perturbative
approaches (the Mirror TBA), and illustrate this explicitly on two such
asymptotically degenerate states.Comment: v3, 20 pages, 1 figure, 2 tables, as publishe
The Spectrum of Strings on Warped AdS_3 x S^3
String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation
which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x
U(1)_L. The holographic dual is an exotic and only partially understood type of
two-dimensional CFT with a reduced unbroken global conformal symmetry group. In
this paper we study the deformed theory on the string worldsheet. It is found
to be related by a spectral flow which is nonlocal in spacetime to the
undeformed worldsheet theory. An exact formula for the spectrum of massive
strings is presented.Comment: 26 pages, no figure
Comments on the Mirror TBA
We discuss various aspects of excited state TBA equations describing the
energy spectrum of the AdS_5 \times S^5 strings and, via the AdS/CFT
correspondence, the spectrum of scaling dimensions of N = 4 SYM local
operators. We observe that auxiliary roots which are used to partially
enumerate solutions of the Bethe-Yang equations do not play any role in
engineering excited state TBA equations via the contour deformation trick. We
further argue that the TBA equations are in fact written not for a particular
string state but for the whole superconformal multiplet, and, therefore, the
psu(2,2|4) invariance is built in into the TBA construction.Comment: 28 pages, 1 figure, v2: misprints are correcte
Twist operators in N=4 beta-deformed theory
In this paper we derive both the leading order finite size corrections for
twist-2 and twist-3 operators and the next-to-leading order finite-size
correction for twist-2 operators in beta-deformed SYM theory. The obtained
results respect the principle of maximum transcendentality as well as
reciprocity. We also find that both wrapping corrections go to zero in the
large spin limit. Moreover, for twist-2 operators we studied the pole structure
and compared it against leading BFKL predictions.Comment: 17 pages; v2: minor changes, references adde
Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
We discuss classical integrable structure of two-dimensional sigma models
which have three-dimensional Schrodinger spacetimes as target spaces. The
Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The
original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R
due to the deformation. According to this symmetry, there are two descriptions
to describe the classical dynamics of the system, 1) the SL(2,R)_L description
and 2) the enhanced U(1)_R description. In the former 1), we show that the
Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a
Lax pair is constructed with the improved current and the classical
integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we
find a non-local current by using a scaling limit of warped AdS_3 and that it
enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is
presented and the corresponding r/s-matrices are also computed. The two
descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde
On the classical equivalence of monodromy matrices in squashed sigma model
We proceed to study the hybrid integrable structure in two-dimensional
non-linear sigma models with target space three-dimensional squashed spheres. A
quantum affine algebra and a pair of Yangian algebras are realized in the sigma
models and, according to them, there are two descriptions to describe the
classical dynamics 1) the trigonometric description and 2) the rational
description, respectively. For every description, a Lax pair is constructed and
the associated monodromy matrix is also constructed. In this paper we show the
gauge-equivalence of the monodromy matrices in the trigonometric and rational
description under a certain relation between spectral parameters and the
rescalings of sl(2) generators.Comment: 32pages, 3figures, references added, introduction and discussion
sections revise
On the six-dimensional origin of the AGT correspondence
We argue that the six-dimensional (2,0) superconformal theory defined on M
\times C, with M being a four-manifold and C a Riemann surface, can be twisted
in a way that makes it topological on M and holomorphic on C. Assuming the
existence of such a twisted theory, we show that its chiral algebra contains a
W-algebra when M = R^4, possibly in the presence of a codimension-two defect
operator supported on R^2 \times C \subset M \times C. We expect this structure
to survive the \Omega-deformation.Comment: References added. 14 page
Double-logs, Gribov-Lipatov reciprocity and wrapping
We study analytical properties of the five-loop anomalous dimension of
twist-2 operators at negative even values of Lorentz spin. Following L. N.
Lipatov and A. I. Onishchenko, we have found two possible generalizations of
double-logarithmic equation, which allow to predict a lot of poles of anomalous
dimension of twist-2 operators at all orders of perturbative theory from the
known results. Second generalization is related with the reciprocity-respecting
function, which is a single-logarithmic function in this case. We have found,
that the knowledge of first orders of the reciprocity-respecting function gives
all-loop predictions for the highest poles. Obtained predictions can be used
for the reconstruction of a general form of the wrapping corrections for
twist-2 operators.Comment: 17 pages, references adde
Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime
dimensions is investigated by means of Monte Carlo simulations. We argue that
it is impossible to construct a lattice action that implements both the O(3)
symmetry as well as at least one supersymmetry exactly at finite lattice
spacing. It is shown by explicit calculations that previously proposed
discretizations fail to reproduce the exact symmetries of the target manifold
in the continuum limit. We provide an alternative lattice action with exact
O(3) symmetry and compare two approaches based on different derivative
operators. Using the nonlocal SLAC derivative for the quenched model on
moderately sized lattices we extract the value {\sigma}(2, u_0) = 1.2604(13)
for the step scaling function at u_0 = 1.0595, to be compared with the exact
value 1.261210. For the supersymmetric model with SLAC derivative the discrete
chiral symmetry is maintained but we encounter strong sign fluctuations,
rendering large lattice simulations ineffective. By applying the Wilson
prescription, supersymmetry and chiral symmetry are broken explicitly at finite
lattice spacing, though there is clear evidence that both are restored in the
continuum limit by fine tuning of a single mass parameter.Comment: 35 pages, 36 figures, 2 tables; updated version as accepted by JHE
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