1,726 research outputs found

    The Geometrodynamics of Sine-Gordon Solitons

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    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

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    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 λR2=4π/k\lambda^{2}_{R}=4\pi/k for any integer k>1k>1: the minimal S-matrix associated with the Lie algebra ak1a_{k-1}. 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(2)/U(1)(2)/{\rm U}(1) coset model at level kk perturbed by its first thermal operator.Comment: SWAT-4

    Towards the Construction of Wightman Functions of Integrable Quantum Field Theories

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    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

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    {\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 q(0)q_{(0)} and the associated solution of the linear system Ψ(0)(λ)\Psi^{(0)} (\lambda), and we construct a new solution Ψ(λ)\Psi(\lambda) differing from Ψ(0)(λ)\Psi^{(0)}(\lambda) by a rational matrix in λ\lambda with at least four poles λ0,1/λ0,λ0,1/λ0\lambda_{0},1/\lambda_{0},\lambda_{0}^*,1/\lambda_{0}^*. The periodi- city condition for closed strings restrict λ0\lambda _{0} to discrete values expressed in terms of Pythagorean numbers. Here we explicitly construct solu- tions depending on (2+1)(2+1)-spacetime coordinates, two arbitrary complex numbers (the 'polarization vector') and two integers (n,m)(n,m) which determine the string windings in the space. The solutions are depicted in the hyperboloid coor- dinates qq and in comoving coordinates with the cosmic time TT. 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 τ\tau turns to be a multivalued function of TT.(This has no analogue in flat space- time).One string is stable (its proper size tends to a constant for TT\to\infty , and its comoving size contracts); the other strings are unstable (their proper sizes blow up for TT\to\infty, 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

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    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

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    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

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    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

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    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

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    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
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