391 research outputs found
Planckian space is an exact solution of the semiclassical Einstein equations
The product space configuration (with and being
radiuses of the components) carrying the electric charge is demonstrated to
be an exact solution of the semiclassical Einstein equations in presence of the
Maxwell field. If the logarithmic UV divergences are absent in the
four-dimensional theory the solution we find is identical to the classical
Bertotti-Robinson space () with no quantum corrections added. In
general, the analysis involves the quadratic curvature coupling
appearing in the effective action. The solutions we find are of the following
types: i) (for arbitrary ) charged configuration which is quantum
deformation of the Bertotti-Robinson space; ii) () Q=0
configuration with and being of the Planck order; iii)
() configuration ( and are of the Planck
order) not connected analytically to the Bertotti-Robinson space. The
interpretation of the solutions obtained and an indication on the internal
structure of the Schwarzschild black hole are discussed.Comment: 14 pages, latex, 1 figure; v2: a note on S2*S2 type solutions adde
Puzzles of eta-deformed AdS_5 x S^5
We derive the part of the Lagrangian for the sigma model on the eta-deformed
AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on
bosons. We then show that there exists a field redefinition which brings the
corresponding Lagrangian to the standard form of type IIB Green-Schwarz
superstring. Reading off the corresponding RR couplings, we observe that they
fail to satisfy the supergravity equations of motion, despite the presence of
kappa-symmetry. However, in a special scaling limit our solution reproduces the
supergravity background found by Maldacena and Russo. Further, using the
fermionic Lagrangian, we compute a number of new matrix elements of the tree
level world-sheet scattering matrix. We then show that after a unitary
transformation on the basis of two-particle states which is not one-particle
factorisable, the corresponding T-matrix factorises into two equivalent parts.
Each part satisfies the classical Yang-Baxter equation and coincides with the
large tension limit of the q-deformed S-matrix.Comment: 59 pages, 1 figure, v2: minor correction
Five-loop Konishi from the Mirror TBA
We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5
mirror model to derive the five-loop anomalous dimension of the Konishi
operator. We show numerically that the corresponding result perfectly agrees
with the one recently obtained via the generalized Luscher formulae. This
constitutes an important test of the AdS/CFT TBA system.Comment: 14 pages, 2 figures, v2: published versio
Towards 4-point correlation functions of any 1/2-BPS operators from supergravity
The quartic effective action for Kaluza-Klein modes that arises upon
compactification of type IIB supergravity on the five-sphere S^5 is a starting
point for computing the four-point correlation functions of arbitrary weight
1/2-BPS operators in N=4 super Yang-Mills theory in the supergravity
approximation. The apparent structure of this action is rather involved, in
particular it contains quartic terms with four derivatives which cannot be
removed by field redefinitions. By exhibiting intricate identities between
certain integrals involving spherical harmonics of S^5 we show that the net
contribution of these four-derivative terms to the effective action vanishes.
Our result is in agreement with and provides further support to the recent
conjecture on the Mellin space representation of the four-point correlation
function of any 1/2-BPS operators in the supergravity approximation.Comment: 12 page
Deformations of nonrelativistic models
The light-cone gauge approach to deformed models is used to
derive the deformed matrix nonlinear Schr\"odinger equation,
the Landau--Lifshitz equation, and the Gardner equation. Properties of
one-soliton solutions of the deformed nonlinear Schr\"odinger
and Korteweg--de Vries equations are discussed in detail. The NLS soliton
exhibits the recently discussed phenomenon of widening/narrowing width of
particles under the deformation. However, whether the soliton's
size is increasing or decreasing depends not only on the sign of the
deformation parameter but also on soliton and potential parameters. The
deformed KdV equation admits a one-parameter family of
one-soliton solutions in addition to the usual velocity parameter. The extra
parameter modifies the properties of the soliton, in particular, it appears in
the dispersion relation.Comment: 34 pages, many figures. V2: minor corrections. V3: Two new comment
sections added, accepted for publication in JHE
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