381 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
Chirality and fermion number in a knotted soliton background
We consider the coupling of a single Dirac fermion to the three component
unit vector field which appears as an order parameter in the Faddeev model.
Classically, the coupling is determined by requiring that it preserves a
certain local frame independence. But quantum mechanically the separate left
and right chiral fermion number currents suffer from a frame anomaly. We employ
this anomaly to compute the fermion number of a knotted soliton. The result
coincides with the self-linking number of the soliton. In particular, the
anomaly structure of the fermions relates directly to the inherent chiral
properties of the soliton. Our result suggests that interactions between
fermions and knotted solitons can lead to phenomena akin the Callan-Rubakov
effect
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
Asymptotically Free Yang-Mills Classical Mechanics with Self-Linked Orbits
We construct a classical mechanics Hamiltonian which exhibits spontaneous
symmetry breaking akin the Coleman-Weinberg mechanism, dimensional
transmutation, and asymptotically free self-similarity congruent with the
beta-function of four dimensional Yang-Mills theory. Its classical equations of
motion support stable periodic orbits and in a three dimensional projection
these orbits are self-linked into topologically nontrivial, toroidal knots.Comment: 9 pages incl. 5 fig
Beyond cusp anomalous dimension from integrability
We study the first sub-leading correction to the cusp
anomalous dimension in the high spin expansion of finite twist operators in
SYM theory. Since this approximation is still governed by a linear
integral equation (derived already from the Bethe Ansatz equations in a
previous paper), we finalise it better in order to study the weak and strong
coupling regimes. In fact, we emphasise how easily the weak coupling expansion
can be obtained, confirms the known four loop result and predicts the higher
orders. Eventually, we pay particular attention to the strong coupling regime
showing agreement and predictions in comparison with string expansion;
speculations on the 'universal' part (upon subtracting the collinear anomalous
dimension) are brought forward.Comment: Latex versio
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
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
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