91 research outputs found
The Bethe ansatz for superconformal Chern-Simons
We study the anomalous dimensions for scalar operators for a
three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We
show that the mixing matrix at two-loop order is that for an integrable
Hamiltonian of an SU(4) spin chain with sites alternating between the
fundamental and the anti-fundamental representations. We find a set of Bethe
equations from which the anomalous dimensions can be determined and give a
proposal for the Bethe equations to the full superconformal group of
OSp(2,2|6).Comment: 22 pages, 9 figures; v2 Overall normalization of the Hamiltonian
corrected and missing diagram contributing to two-site interactions included.
Typos fixed; v3 Figure 8 corrected; v4 Misprints corrected; v5 Correct
figures recovered. Published version; v6: misprints in (3.15), (3.16), (3.17)
correcte
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
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
A note on spin chain/string duality
Recently a significant progress in matching the anomalous dimensions of
certain class of operators in N=4 SYM theory and rotating strings was made. The
correspondence was established mainly using Bethe ansatz technique applied to
the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203)
suggested to solve the Heisenberg model by using of sigme model approach. In
this paper we generalize the solutions obtained by Kruczenski and comment on
the dual string theory. It turns out that our solutions are related to the so
called Neumann-Rosochatius integrable system. We comment on the spin chain
solutions and on the string/gauge theory correspondence.Comment: v.2 One reference added, typos corrected, 21 page
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
Holographic 3-point function at one loop
We explore the recent weak/strong coupling match of three-point functions in
the AdS/CFT correspondence for two semi-classical operators and one light
chiral primary operator found by Escobedo et al. This match is between the
tree-level three-point function with the two semi-classical operators described
by coherent states while on the string side the three-point function is found
in the Frolov-Tseytlin limit. We compute the one-loop correction to the
three-point function on the gauge theory side and compare this to the
corresponding correction on the string theory side. We find that the
corrections do not match. Finally, we discuss the possibility of further
contributions on the gauge theory side that can alter our results.Comment: 24 pages, 2 figures. v2: Typos fixed, Ref. added, figure improved.
v3: Several typos and misprints fixed, Ref. updated, figures improved, new
section 2.3 added on correction from spin-flipped coherent state,
computations on string theory side improve
Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains
We present an integrability-preserving recursion relation for the explicit
construction of long-range spin chain Hamiltonians. These chains are
generalizations of the Haldane-Shastry and Inozemtsev models and they play an
important role in recent advances in string/gauge duality. The method is based
on arbitrary nearest-neighbour integrable spin chains and it sheds light on the
moduli space of deformation parameters. We also derive the closed chain
asymptotic Bethe equations.Comment: 10 pages, v2: reference added, minor changes, v3: published version
with added/updated reference
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
Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
Motivated by the desire to relate Bethe ansatz equations for anomalous
dimensions found on the gauge theory side of the AdS/CFT correspondence to
superstring theory on AdS_5 x S5 we explore a connection between the asymptotic
S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum
field theory. The latter generalizes the standard ``non-relativistic''
Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic
Heisenberg spin chain and should be related to a limit of superstring effective
action. We find the exact form of the quartic interaction terms in the
generalized LL type action whose quantum
S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin
chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders
in the `t Hooft coupling an earlier computation of Klose and Zarembo of the
S-matrix of the standard LL model. We also consider a generalization to the
case when the spin chain S-matrix contains an extra ``string'' phase and
determine the exact form of the LL 4-vertex corresponding to the low-energy
limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the
relation between the resulting ``non-relativistic'' non-local action and the
second-derivative string sigma model. We comment on modifications introduced by
strong-coupling corrections to the AFS phase. We mostly discuss the SU(2)
sector but also present generalizations to the SL(2) and SU(1|1) sectors,
confirming universality of the dressing phase contribution by matching the
low-energy limit of the AFS-type spin chain S-matrix with tree-level
string-theory S-matrix.Comment: 52 pages, 4 figures, Imperial-TP-AT-6-2; v2: new sections 7.3 and 7.4
computing string tree-level S-matrix in SL(2) and SU(1|1) sectors, references
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