92 research outputs found
The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
Using the quantum string Bethe ansatz we derive the one-loop energy of a
folded string rotating with angular momenta (S,J) in AdS_3 x S^1 inside AdS_5 x
S^5 in the limit 1 << J << S, z=\lambda^(1/2) log(S/J) /(\pi J) fixed. The
one-loop energy is a sum of two contributions, one originating from the
Hernandez-Lopez phase and another one being due to spin chain finite size
effects. We find a result which at the functional level exactly matches the
result of a string theory computation. Expanding the result for large z we
obtain the strong coupling limit of the scaling function for low twist, high
spin operators of the SL(2) sector of N=4 SYM. In particular we recover the
famous -3 log(2)/\pi. Its appearance is a result of non-trivial cancellations
between the finite size effects and the Hernandez-Lopez correction.Comment: 18 pages, one figure, v2: footnote changed, v3: reference added, typo
correcte
Four-dimensional Hall mechanics as a particle on \DC P^3
In order to establish an explicit connection between four-dimensional Hall
effect on and six-dimensional Hall effect on \DC P^3, we perform the
Hamiltonian reduction of a particle moving on \DC P^3 in a constant magnetic
field to the four-dimensional Hall mechanics (i.e. a particle on in a
SU(2) instanton field). This reduction corresponds to fixing the isospin of the
latter system.Comment: 7 pages, LaTeX file, no figures, PACS numbers: 03.65-w, 11.30.P
Renormalisability of T-dualised non-homogeneous sigma-models
The quantum equivalence between -models and their non-abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group . We prove that the one-loop renormalisability of the initial torsionless -models does still imply the one-loop renormalisability of the T-dualised torsionful model. A kind of new ``dilaton anomaly'' appears for T-dualised quasi-Einstein metrics which never occurs in the framework of T-dualised homogeneous Einstein metrics
Singular 7-manifolds with G_2 holonomy and intersecting 6-branes
A 7-manifold with G_2 holonomy can be constructed as a R^3 bundle over a
quaternionic space. We consider a quaternionic base space which is singular and
its metric depends on three parameters, where one of them corresponds to an
interpolation between S^4 and CP^2 or its non-compact analogs. This 4-d
Einstein space has four isometries and the fixed point set of a generic Killing
vector is discussed. When embedded into M-theory the compactification over a
given Killing vector gives intersecting 6-branes as IIA configuration and we
argue that membrane instantons may resolve the curvature singularity.Comment: 20 pages, 2 figures, Latex, add reference
U(1) x U(1) Quaternionic Metrics from Harmonic Superspace
We construct, using harmonic superspace and the quaternionic quotient
approach, a quaternionic-K\"ahler extension of the most general two centres
hyper-K\"ahler metric. It possesses isometry, contains as
special cases the quaternionic-K\"ahler extensions of the Taub-NUT and
Eguchi-Hanson metrics and exhibits an extra one-parameter freedom which
disappears in the hyper-K\"ahler limit. Some emphasis is put on the relation
between this class of quaternionic-K\"ahler metrics and self-dual Weyl
solutions of the coupled Einstein-Maxwell equations. The relation between our
explicit results and the recent general ansatz of Calderbank and Pedersen for
quaternionic-K\"ahler metrics with isometries is traced in
detail.Comment: 40 pages,0 figure Minor corrected typo
Quasilocality of joining/splitting strings from coherent states
Using the coherent state formalism we calculate matrix elements of the
one-loop non-planar dilatation operator of SYM between operators
dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior.
We comment on the {\it qualitative} similarity of our matrix elements to the
interaction vertex of a string field theory. In addition, we present a solvable
toy model for string splitting and joining. The scaling behaviour of the matrix
elements suggests that the contribution to the genus one energy shift coming
from semi-classical string splitting and joining is small.Comment: 17 pages, 7 figures in 11 file
Strong coupling for planar SYM theory: an all-order result
We propose a scheme for determining a generalised scaling function, namely
the Sudakov factor in a peculiar double scaling limit for high spin and large
twist operators belonging to the sector of planar SYM. In
particular, we perform explicitly the all-order computation at strong 't Hooft
coupling regarding the first (contribution to the) generalised scaling
function. Moreover, we compare our asymptotic results with the numerical
solutions finding a very good agreement and evaluate numerically the
non-asymptotic contributions. Eventually, we illustrate the agreement and
prediction on the string side.Comment: references added, typos corrected; Latex file plus one figur
Quaternionic Extension of the Double Taub-NUT Metric
Starting from the generic harmonic superspace action of the
quaternion-K\"ahler sigma models and using the quotient approach we present, in
an explicit form, a quaternion-K\"ahler extension of the double Taub-NUT
metric. It possesses isometry and supplies a new example of
non-homogeneous Einstein metric with self-dual Weyl tensor.Comment: 12 pages, 0 figure, latex file, to appear in Phys. Lett.B, reference
corrected, Dubna preprint number adde
Quantum structure of T-dualized models with symmetry breaking
We study the principal sigma-models defined on any group manifold GL x GR/GD
with breaking of GR, and their T-dual transforms. For abritary breaking we can
express the torsion and Ricci tensor of the dual model in terms of the frame
geometry of the initial principal model. Using these results, we give necessary
and sufficient conditions for the dual model to be torsionless and prove that
the one-loop renormalizability of a given principal model is inherited by its
dual partner, who shares the same beta-functions. These results are shown to
hold also if the principal model is endowed with torsion. As an application we
compute the beta-functions for the full Bianchi family and show that for some
choices of the breaking parameters the dilaton anomaly is absent: for these
choices the dual torsion vanishes. For the dualized Bianchi V model (which is
torsionless for any breaking), we take advantage of its simpler structure, to
study its two-loops renormalizability.Comment: 24 pages, no figures, latex2
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