220 research outputs found
Bethe Ansatz for a Quantum Supercoset Sigma Model
We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog
to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for
this system, we obtain integral equations for states of large particle density
in an SU(2) sector, which are exact in the sigma model coupling constant. As a
check, we derive as a limit the general classical Bethe equation of Kazakov,
Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions
around the well-studied classical limit, the lambda^{-1/2} effects and the 1/J
effects. Our approach captures the first type, but not the second.Comment: 30 pages, 1 figure, v2: references adde
AdS/CFT duality at strong coupling
We study the strong coupling limit of AdS/CFT correspondence in the framework
of a recently proposed fermionic formulation of the Bethe Ansatz equations
governing the gauge theory anomalous dimensions. We provide examples of states
that do not follow the Gubser-Klebanov-Polyakov law at large 't Hooft coupling
, in contrast with recent results on the quantum string Bethe
equations valid in that regime. This result indicates that the fermionic
construction cannot be trusted at large , although it remains an
efficient tool to compute the weak coupling expansion of anomalous dimensions.Comment: Presented at Nonlinear Physics. Theory and Experiment. IV Gallipoli,
June 22 - July 1, 2006. To appear in the proceeding
On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
The Bethe equations, arising in description of the spectrum of the dilatation
operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are
considered in the anti-ferromagnetic regime. These equations are deformation of
those for the Heisenberg XXX magnet. It is proven that in the thermodynamic
limit roots of the deformed equations group into strings. It is proven that the
corresponding Yang's action is convex, which implies uniqueness of solution for
centers of the strings. The state formed of strings of length (2n+1) is
considered and the density of their distribution is found. It is shown that the
energy of such a state decreases as n grows. It is observed that
non-analyticity of the left hand side of the Bethe equations leads to an
additional contribution to the density and energy of strings of even length.
Whence it is concluded that the structure of the anti-ferromagnetic vacuum is
determined by the behaviour of exponential corrections to string solutions in
the thermodynamic limit and possibly involves strings of length 2.Comment: LaTex, 9 pages, 1 figur
Fluctuations and Energy Shifts in the Bethe Ansatz
We study fluctuations and finite size corrections for the ferromagnetic
thermodynamic limit in the Bethe ansatz for the Heisenberg XXX1/2 spin chain,
which is the AdS/CFT dual of semiclassical spinning strings. For this system we
derive the standard quantum mechanical formula which expresses the energy shift
as a sum over fluctuation energies. As an example we apply our results to the
simplest, one-cut solution of this system and derive its spectrum of
fluctuations.Comment: 8 pages, 1 figure, v2: comparison to string theory improved,
reference adde
Fine Structure of String Spectrum in AdS(5)xS(5)
The spectrum of an infinite spinning string in AdS(5) does not precisely
match the spectrum of dual gauge theory operators, interpolated to the strong
coupling regime with the help of Bethe-ansatz equations. We show that the
mismatch is due to interactions in the string sigma-model which cannot be
neglected even at asymptotically large 't Hooft coupling.Comment: 4 pages, 1 figure; v2: IR safety conditions spelled out more
precisely; v3: eq. (14) correcte
Correlation functions, null polygonal Wilson loops, and local operators
We consider the ratio of the correlation function of n+1 local operators over
the correlator of the first n of these operators in planar N=4 super-Yang-Mills
theory, and consider the limit where the first n operators become pairwise null
separated. By studying the problem in twistor space, we prove that this is
equivalent to the correlator of a n-cusp null polygonal Wilson loop with the
remaining operator in general position, normalized by the expectation value of
the Wilson loop itself, as recently conjectured by Alday, Buchbinder and
Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such
correlators. Finally, we study the natural extension where n operators become
pairwise null separated with k operators in general position. As an example, we
perform an analysis of the resulting correlator for k=2 and discuss some of the
difficulties associated to fixing the correlator completely in the strong
coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3:
published versio
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
New Integrable Structures in Large-N QCD
We study the anomalous dimensions of single trace operators composed of field
strengths in large-N QCD. The matrix of anomalous dimensions is
the Hamiltonian of a compact spin chain with two spin one representations at
each vertex corresponding to the selfdual and anti-selfdual components of
. Due to the special form of the interaction it is possible to
study separately renormalization of purely selfdual components. In this sector
the Hamiltonian is integrable and can be exactly solved by Bethe ansatz. Its
continuum limit is described by the level two SU(2) WZW model.Comment: 12 pages; V2: ref. added, V3: refs. added, explicit expression for
the spin ladder and other text improvement
Eliminating ambiguities for quantum corrections to strings moving in
We apply a physical principle, previously used to eliminate ambiguities in
quantum corrections to the 2 dimensional kink, to the case of spinning strings
moving in , thought of as another kind of two
dimensional soliton. We find that this eliminates the ambiguities and selects
the result compatible with AdS/CFT, providing a solid foundation for one of the
previous calculations, which found agreement. The method can be applied to
other classical string "solitons".Comment: 18 pages, latex; references added, comments added at end of section
4, a few words changed; footnote added on page 1
Impure Aspects of Supersymmetric Wilson Loops
We study a general class of supersymmetric Wilson loops operator in N = 4
super Yang-Mills theory, obtained as orbits of conformal transformations. These
loops are the natural generalization of the familiar circular Wilson-Maldacena
operator and their supersymmetric properties are encoded into a Killing spinor
that is not pure. We present a systematic analysis of their scalar couplings
and of the preserved supercharges, modulo the action of the global symmetry
group, both in the compact and in the non-compact case. The quantum behavior of
their expectation value is also addressed, in the simplest case of the
Lissajous contours: explicit computations at weak-coupling, through Feynman
diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence,
suggest the possibility of an exact evaluation.Comment: 40 pages, 4 figure
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