29 research outputs found
The Dressing Factor and Crossing Equations
We utilize the DHM integral representation for the BES dressing factor of the
world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the
crossing equations to fix the principal branch of the dressing factor on the
rapidity torus. The results obtained are further used, in conjunction with the
fusion procedure, to determine the bound state dressing factor of the mirror
theory. We convincingly demonstrate that the mirror bound state S-matrix found
in this way does not depend on the internal structure of a bound state solution
employed in the fusion procedure. This welcome feature is in perfect parallel
to string theory, where the corresponding bound state S-matrix has no bearing
on bound state constituent particles as well. The mirror bound state S-matrix
we found provides the final missing piece in setting up the TBA equations for
the AdS_5xS^5 mirror theory.Comment: LaTex, 48 pages, 10 figures; v2: a new section added where the
dressing factor of the mirror theory is found; v3: formula (6.12) is
corrected, a new figure is added, accepted for publication in J.Phys.
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
We derive a set of integral equations of the TBA type for the generalized
cusp anomalous dimension, or the quark antiquark potential on the three sphere,
as a function of the angles. We do this by considering a family of local
operators on a Wilson loop with charge L. In the large L limit the problem can
be solved in terms of a certain boundary reflection matrix. We determine this
reflection matrix by using the symmetries and the boundary crossing equation.
The cusp is introduced through a relative rotation between the two boundaries.
Then the TBA trick of exchanging space and time leads to an exact equation for
all values of L. The L=0 case corresponds to the cusped Wilson loop with no
operators inserted. We then derive a slightly simplified integral equation
which describes the small angle limit. We solve this equation up to three loops
in perturbation theory and match the results that were obtained with more
direct approaches.Comment: 63 pages, 12 figures. v2: references added, typos correcte
Three-point function of semiclassical states at weak coupling
We give the derivation of the previously announced analytic expression for
the correlation function of three heavy non-BPS operators in N=4
super-Yang-Mills theory at weak coupling. The three operators belong to three
different su(2) sectors and are dual to three classical strings moving on the
sphere. Our computation is based on the reformulation of the problem in terms
of the Bethe Ansatz for periodic XXX spin-1/2 chains. In these terms the three
operators are described by long-wave-length excitations over the ferromagnetic
vacuum, for which the number of the overturned spins is a finite fraction of
the length of the chain, and the classical limit is known as the Sutherland
limit. Technically our main result is a factorized operator expression for the
scalar product of two Bethe states. The derivation is based on a fermionic
representation of Slavnov's determinant formula, and a subsequent bosonisation.Comment: 28 pages, 5 figures, cosmetic changes and more typos corrected in v
Strong coupling from the Hubbard model
It was recently observed that the one dimensional half-filled Hubbard model
reproduces the known part of the perturbative spectrum of planar N=4 super
Yang-Mills in the SU(2) sector. Assuming that this identification is valid
beyond perturbation theory, we investigate the behavior of this spectrum as the
't Hooft parameter \lambda becomes large. We show that the full dimension
\Delta of the Konishi superpartner is the solution of a sixth order polynomial
while \Delta for a bare dimension 5 operator is the solution of a cubic. In
both cases the equations can be solved easily as a series expansion for both
small and large \lambda and the equations can be inverted to express \lambda as
an explicit function of \Delta. We then consider more general operators and
show how \Delta depends on \lambda in the strong coupling limit. We are also
able to distinguish those states in the Hubbard model which correspond to the
gauge invariant operators for all values of \lambda. Finally, we compare our
results with known results for strings on AdS_5\times S^5, where we find
agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added;
typos fixed, minor changes; v3 fixed figures; v4 more references added, minor
correctio
Bethe Ansatz in Stringy Sigma Models
We compute the exact S-matrix and give the Bethe ansatz solution for three
sigma-models which arise as subsectors of string theory in AdS(5)xS(5):
Landau-Lifshitz model (non-relativistic sigma-model on S(2)),
Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and
Faddeev-Reshetikhin model (string sigma-model on S(3)xR).Comment: 37 pages, 11 figure
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
Y-system for Scattering Amplitudes
We compute N=4 Super Yang Mills planar amplitudes at strong coupling by
considering minimal surfaces in AdS_5 space. The surfaces end on a null
polygonal contour at the boundary of AdS. We show how to compute the area of
the surfaces as a function of the conformal cross ratios characterizing the
polygon at the boundary. We reduce the problem to a simple set of functional
equations for the cross ratios as functions of the spectral parameter. These
equations have the form of Thermodynamic Bethe Ansatz equations. The area is
the free energy of the TBA system. We consider any number of gluons and in any
kinematic configuration.Comment: 69 pages, 19 figures, v2: references added, minor addition
Foundations of the AdS_5 x S^5 Superstring. Part I
We review the recent advances towards finding the spectrum of the AdS_5 x S^5
superstring. We thoroughly explain the theoretical techniques which should be
useful for the ultimate solution of the spectral problem. In certain cases our
exposition is original and cannot be found in the existing literature. The
present Part I deals with foundations of classical string theory in AdS_5 x
S^5, light-cone perturbative quantization and derivation of the exact
light-cone world-sheet scattering matrix.Comment: 161 page