135 research outputs found
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
Field Decomposition and the Ground State Structure of SU(2) Yang-Mills Theory
We compute the effective potential of SU(2) Yang-Mills theory using the
background field method and the Faddeev-Niemi decomposition of the gauge
fields. In particular, we find that the potential will depend on the values of
two scalar fields in the decomposition and that its structure will give rise to
a symmetry breaking.Comment: 8 pages, 1 figure. Typos corrected and title change
A Universality Test of the Quantum String Bethe Ansatz
We show that the quantum corrected string Bethe ansatz passes an important
universality test by demonstrating that it correctly incorporates the
non-analytical terms in the string sigma model one-loop correction for rational
three-spin strings with two out of the three spins identical. Subsequently, we
use the quantum corrected string Bethe ansatz to predict the exact form of the
non-analytic terms for the generic rational three-spin string.Comment: 12 pages, references adde
Shafranov's virial theorem and magnetic plasma confinement
Shafranov's virial theorem implies that nontrivial magnetohydrodynamical
equilibrium configurations must be supported by externally supplied currents.
Here we extend the virial theorem to field theory, where it relates to
Derrick's scaling argument on soliton stability. We then employ virial
arguments to investigate a realistic field theory model of a two-component
plasma, and conclude that stable localized solitons can exist in the bulk of a
finite density plasma. These solitons entail a nontrivial electric field which
implies that purely magnetohydrodynamical arguments are insufficient for
describing stable, nontrivial structures within the bulk of a plasma.Comment: 9 pages no figure
Twist-three at five loops, Bethe Ansatz and wrapping
We present a formula for the five-loop anomalous dimension of N=4 SYM
twist-three operators in the sl(2) sector. We obtain its asymptotic part from
the Bethe Ansatz and finite volume corrections from the generalized Luescher
formalism, considering scattering processes of spin chain magnons with virtual
particles that travel along the cylinder. The complete result respects the
expected large spin scaling properties and passes non-trivial tests including
reciprocity constraints. We analyze the pole structure and find agreement with
a conjectured resummation formula. In analogy with the twist-two anomalous
dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large
values of the spin.Comment: 19 page
Anomalous dimensions of finite size field strength operators in N=4 SYM
In the N=4 super Yang-Mills theory, we consider the higher order anomalous
dimensions gamma_L(g) of purely gluonic operators Tr(F^L) where F is a
component of the self-dual field strength. We propose compact closed
expressions depending parametrically on L that reproduce the prediction of
Bethe Ansatz equations up to five loop order, including transcendental dressing
corrections. The size dependence follows a simple pattern as the perturbative
order is increased and suggests hidden relations for these special operators.Comment: 26 pages, 3 eps figures. v2: published version, minor changes,
references adde
From weak coupling to spinning strings
We identify the gauge theory dual of a spinning string of minimal energy with
spins S_1, S_2 on AdS_5 and charge J on S^5. For this purpose we focus on a
certain set of local operators with two different types of covariant
derivatives acting on complex scalar fields. We analyse the corresponding
nested Bethe equations for the ground states in the limit of large spins. The
auxiliary Bethe roots form certain string configurations in the complex plane,
which enable us to derive integral equations for the leading and sub-leading
contribution to the anomalous dimension. The results can be expressed through
the observables of the sl(2) sub-sector, i.e. the cusp anomaly f(g) and the
virtual scaling function B_L(g), rendering the strong-coupling analysis
straightforward. Furthermore, we also study a particular sub-class of these
operators specialising to a scaling limit with finite values of the second spin
at weak and strong coupling.Comment: 23 pages, 3 figures, minor changes, references adde
Star product and the general Leigh-Strassler deformation
We extend the definition of the star product introduced by Lunin and
Maldacena to study marginal deformations of N=4 SYM. The essential difference
from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with
charges in a corresponding diagonal matrix, we consider two Z_3-symmetries
followed by an SU(3) transformation, with resulting off-diagonal elements. From
this procedure we obtain a more general Leigh-Strassler deformation, including
cubic terms with the same index, for specific values of the coupling constants.
We argue that the conformal property of N=4 SYM is preserved, in both beta-
(one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the
deformation for each amplitude can be extracted in a prefactor. We also
conclude that the obtained amplitudes should follow the iterative structure of
MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A
added, v4: clarification in section 3.
Spiky strings in the SL(2) Bethe Ansatz
We study spiky strings in the context of the SL(2) Bethe ansatz equations. We
find an asymmetric distribution of Bethe roots along one cut that determines
the all loop anomalous dimension at leading and subleading orders in a large S
expansion. At leading order in strong coupling (large lambda) we obtain that
the energy of such states is given, in terms of the spin S and the number of
spikes n by E-S=n sqrt{lambda}/(2 pi) (ln 16 pi S/(n sqrt{lambda})+ ln sin
(pi/n) - 1)+ O(ln S/S). This result matches perfectly the same expansion
obtained from the known spiky string classical solution.
We then discuss a two cut spiky string Bethe root distribution at one-loop in
the SL(2) Bethe ansatz. In this case we find a limit where n goes to infinity,
keeping (E+S)/n^2, (E-S)/n, J/n fixed. This is the one loop version of a limit
previously considered in the context of the string classical solutions in AdS5
x S5. In that case it was related to a string solution in the AdS pp-wave
background.Comment: 32 pages, 6 figures; v2: minor corrections, references added; v3:
minor correction
Operator with large spin and spinning D3-brane
We consider the conformal dimension of an operator with large spin, using a
spinning D3-brane with electric flux in AdS_5 x S^5 instead of spinning
fundamental string. This spinning D3-brane solution seems to correspond to an
operator made by taking trace in a large symmetric representation. The
conformal dimension, the spin and the R-charge show a scaling relation in a
certain region of parameters. In the small string charge limit, the result is
consistent with the fundamental string picture. There is a phase transition
when the fundamental string charge become larger than a certain critical value;
there is no stable D3-brane solution above the critical value.Comment: 16 pages, 4 figures. v2: typos corrected, references added, series
expansion of anomalous dimension added. v3: a reference added, comment on
calculation in gauge theor
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