19 research outputs found
Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models
We propose nonlinear integral equations for the finite volume one-particle
energies in the O(3) and O(4) nonlinear sigma-models. The equations are written
in terms of a finite number of components and are therefore easier to solve
numerically than the infinite component excited state TBA equations proposed
earlier. Results of numerical calculations based on the nonlinear integral
equations and the excited state TBA equations agree within numerical precision.Comment: numerical results adde
Hybrid-NLIE for the AdS/CFT spectral problem
Hybrid-NLIE equations, an alternative finite NLIE description for the
spectral problem of the super sigma model of AdS/CFT and its gamma-deformations
are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT
TBA equations by a few appropriately chosen complex NLIE variables, which are
coupled among themselves and to the Y-functions associated to the remaining
central nodes of the TBA diagram. The integral equations are written explicitly
for the ground state of the gamma-deformed system. We linearize these NLIE
equations, analytically calculate the first correction to the asymptotic
solution and find agreement with analogous results coming from the original TBA
formalism. Our equations differ substantially from the recently published
finite FiNLIE formulation of the spectral problem.Comment: 63 pages, 1 figur
Konishi operator at intermediate coupling
TBA equations for two-particle states from the sl(2) sector proposed by
Arutyunov, Suzuki and the author are solved numerically for the Konishi
operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained
is used to analyze the properties of Y-functions and address the issue of the
existence of the critical values of the coupling. In addition we find a new
integral representation for the BES dressing phase which substantially reduces
the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not
vanis
Contour deformation trick in hybrid NLIE
The hybrid NLIE of AdS_5 x S^5 is applied to a wider class of states. We find
that the Konishi state of the orbifold AdS_5 x (S^5/Z_S) satisfies A_1 NLIE
with the source terms which are derived from contour deformation trick. For
general states, we construct a deformed contour with which the contour
deformation trick yields the correct source terms.Comment: 39 pages, 6 figures, v2: discussion on analyticity constraints
replaced by consistent deformed contou
TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
The ground-state energy of integrably-twisted theories is analyzed in finite
volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type
corrections for large volumes of the vacuum energy for integrable theories with
twisted boundary conditions and twisted S-matrix. We then derive the twisted
thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground
state, from which we obtain an untwisted Y-system. The two approaches are
compared by expanding the TBA equations to NLO, and exact agreement is found.
We give explicit results for the O(4) model and for the three-parameter family
of -deformed (non-supersymmetric) planar AdS/CFT model, where the
ground-state energy can be nontrivial and can acquire finite-size corrections.
The NLO corrections, which correspond to double-wrapping diagrams, are
explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
We use the string hypothesis for the mirror theory to derive the
Thermodynamic Bethe Ansatz equations for the AdS_5 x S^5 mirror model. We
further demonstrate how these equations can be used to construct the associated
Y-system recently discussed in the literature, putting particular emphasis on
the assumptions and the range of validity of the corresponding construction.Comment: 31 pages, LaTex, v2: references added, v3: published versio
Exploring the mirror TBA
We apply the contour deformation trick to the Thermodynamic Bethe Ansatz
equations for the AdS_5 \times S^5 mirror model, and obtain the integral
equations determining the energy of two-particle excited states dual to N=4 SYM
operators from the sl(2) sector. We show that each state/operator is described
by its own set of TBA equations. Moreover, we provide evidence that for each
state there are infinitely-many critical values of 't Hooft coupling constant
\lambda, and the excited states integral equations have to be modified each
time one crosses one of those. In particular, estimation based on the large L
asymptotic solution gives \lambda \approx 774 for the first critical value
corresponding to the Konishi operator. Our results indicate that the related
calculations and conclusions of Gromov, Kazakov and Vieira should be
interpreted with caution. The phenomenon we discuss might potentially explain
the mismatch between their recent computation of the scaling dimension of the
Konishi operator and the one done by Roiban and Tseytlin by using the string
theory sigma model.Comment: 69 pages, v2: new "hybrid" equations for YQ-functions, figures and
tables are added. Analyticity of Y-system is discussed, v3: published versio
Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu
and sigma models. We find evidence that the GN S matrix proposed by Bassi and
Leclair [12] is the correct one. We determine features of the sigma model S
matrix, which seem highly unconventional; we conjecture in particular a
relation between this sigma model and the complex sine-Gordon model at a
particular value of the coupling. We uncover an intriguing duality between the
OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN
model) on the other, somewhat generalizing to the massive case recent results
on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into
the random bond Ising model proposed by Cabra et al. [39], and conclude that
their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio
String hypothesis for the AdS_5 x S^5 mirror
We discuss the states which contribute in the thermodynamic limit of the
mirror theory, the latter is obtained from the light-cone gauge-fixed string
theory in the AdS_5 x S^5 background by the double-Wick rotation. We analyze
the Bethe-Yang equations for the mirror theory and formulate the string
hypothesis. We show that in the thermodynamic limit solutions of the Bethe-Yang
equations arrange themselves into Bethe string configurations similar to the
ones appearing in the Hubbard model. We also derive a set of equations
describing the bound states and the Bethe string configurations of the mirror
theory.Comment: LaTex, 18 pages, typos are correcte