1,726 research outputs found
The Geometrodynamics of Sine-Gordon Solitons
The relationship between N-soliton solutions to the Euclidean sine-Gordon
equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is
investigated, with emphasis on the important role played by the dilaton in
determining the black hole geometry. We show how an N-soliton solution can be
used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and
construct the transformation to more standard ``Schwarzchild-like''
coordinates. For N=1 and 2, we find explicit closed form solutions to the
dilaton equations of motion in soliton coordinates, and find the relationship
between the soliton parameters and the black hole mass. Remarkably, the black
hole mass is non-negative for arbitrary soliton parameters. In the one-soliton
case the coordinates are shown to cover smoothly a region containing the whole
interior of the black hole as well as a finite neighbourhood outside the
horizon. A Hamiltonian analysis is performed for slicings that approach the
soliton coordinates on the interior, and it is shown that there is no boundary
contribution from the interior. Finally we speculate on the sine-Gordon
solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include
Quantum scattering of charged solitons in the complex sine-Gordon model
The scattering of charged solitons in the complex sine-Gordon field theory is
investigated. An exact factorizable S-matrix for the theory is proposed when
the renormalized coupling constant takes the values
for any integer : the minimal S-matrix associated with the Lie algebra
. It is shown that the proposed S-matrix reproduces the leading
semiclassical behaviour of all amplitudes in the theory and is the minimal
S-matrix which is consistent with the semiclassical spectrum of the model. The
results are completely consistent with the description of the complex
sine-Gordon theory as the SU coset model at level perturbed
by its first thermal operator.Comment: SWAT-4
Towards the Construction of Wightman Functions of Integrable Quantum Field Theories
The purpose of the ``bootstrap program'' for integrable quantum field
theories in 1+1 dimensions is to construct a model in terms of its Wightman
functions explicitly. In this article, this program is mainly illustrated in
terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the
scaling Ising model. We review some previous results on sine-Gordon breather
form factors and quantum operator equations. The problem to sum over
intermediate states is attacked in the short distance limit of the two point
Wightman function for the sinh-Gordon and the scaling Ising model.Comment: LATEX 18 pages, Talk presented at the '6th International Workshop on
Conformal Field Theories and Integrable Models', in Chernologka, September
200
Multi-String Solutions by Soliton Methods in De Sitter Spacetime
{\bf Exact} solutions of the string equations of motion and constraints are
{\bf systematically} constructed in de Sitter spacetime using the dressing
method of soliton theory. The string dynamics in de Sitter spacetime is
integrable due to the associated linear system. We start from an exact string
solution and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . Despite of
the fact that we have a single world sheet, our solutions describe {\bf multi-
ple}(here five) different and independent strings; the world sheet time
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , while their comoving sizes tend to cons-
tants). These solutions (even the stable strings) do not oscillate in time. The
interpretation of these solutions and their dynamics in terms of the sinh-
Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under
reques
The "Bootstrap Program" for Integrable Quantum Field Theories in 1+1 Dim
The purpose of the "bootstrap program" is to construct integrable quantum
field theories in 1+1 dimensions in terms of their Wightman functions
explicitly. As an input the integrability and general assumptions of local
quantum field theories are used. The object is to be achieved in tree steps: 1)
The S-matrix is obtained using a qualitative knowledge of the particle spectrum
and the Yang-Baxter equations. 2) Matrix elements of local operators are
calculated by means of the "form factor program" using the S-matrix as an
input. 3) The Wightman functions are calculated by taking sums over
intermediate states. The first step has been performed for a large number of
models and also the second one for several models. The third step is unsolved
up to now. Here the program is illustrated in terms of the sine-Gordon model
alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we
propose general formulae for form factors. For example the n-particle matrix
element for all higher currents are given and in particular all eigenvalues of
the higher conserved charges are calculated. Furthermore quantum operator
equations are obtained in terms of their matrix elements, in particular the
quantum sine-Gordon field equation. Exact expressions for the finite wave
function and mass renormalization constants are calculated.Comment: Latex, 23 page
Generating AdS String Solutions
We use a Pohlmeyer type reduction to generate classical string solutions in
AdS spacetime. In this framework we describe a correspondence between spikes in
AdS_3 and soliton profiles of the sinh-Gordon equation. The null cusp string
solution and its closed spinning string counterpart are related to the
sinh-Gordon vacuum. We construct classical string solutions corresponding to
sinh-Gordon solitons, antisolitons and breathers by the inverse scattering
technique. The breather solutions can also be reproduced by the sigma model
dressing method.Comment: 21 pages, 3 figures, references adde
Noncommutative Integrable Field Theories in 2d
We study the noncommutative generalization of (euclidean) integrable models
in two-dimensions, specifically the sine- and sinh-Gordon and the U(N)
principal chiral models. By looking at tree-level amplitudes for the
sinh-Gordon model we show that its na\"\i ve noncommutative generalization is
{\em not} integrable. On the other hand, the addition of extra constraints,
obtained through the generalization of the zero-curvature method, renders the
model integrable. We construct explicit non-local non-trivial conserved charges
for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber
method.Comment: 18 pages, 1 figure; v2: references adde
Giant Holes
We study the semiclassical spectrum of excitations around a long spinning
string in AdS_3. In addition to the usual small fluctuations, we find the
spectrum contains a branch of solitonic excitations of finite energy. We
determine the dispersion relation for these excitations. This has a
relativistic form at low energies but also matches the dispersion relation for
the "hole" of the dual gauge theory spin chain at high energies. The low-energy
behaviour is consistent with the hypothesis that the solitonic excitations
studied here are continuously related to the elementary excitations of the
string.Comment: 17 pages, 1 figure; additional references include
Moduli Dynamics of AdS_3 Strings
We construct a general class of solutions for a classical string in AdS_3
spacetime. The construction is based on a Pohlmeyer type reduction, with the
sinh-Gordon model providing the general N-soliton solutions. The corresponding
exact spiky string configurations are then reconstructed through the inverse
scattering method. It is shown that the string moduli are determined entirely
by those of the solitons.Comment: 22 pages, no figures; references adde
- …