In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat surface. In this paper, we derive renormalization-group recursion relations for the sine-Gordon model using field-theoretic techniques developed to study flat spac...

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, β2 =4π. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable. The one-dimensional (1D) quantum sine...

Let q(x, t) satisfy an integrable nonlinear evolution PDE on the interval 0 < x < L, and let the order of the highest x-derivative be n. For a problem to be at least linearly well-posed one must prescribe N boundary conditions at x = 0 and n − N boundary conditions at x = L, where if n is even, N = n/2, and if n is odd, N is either (n − 1)/2 or (n + 1)/2, depending on the sign of ∂n x q. For ex...

We propose nonlinear integral equations to describe the groundstate energy of the fractional supersymmetric sine-Gordonmodels. The equations encompass theN = 1 supersymmetric sine-Gordonmodel as well as the φid,id,adj perturbation of the SU(2)L×SU(2)K/SU(2)L+K models at rational level K. A second set of equations are proposed for the groundstate energy of the N = 2 supersymmetric sine-Gordon mo...

We study the properties of the double-frequency sine–Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, ...

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and ex...

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection R-matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine-Gordon model, is given. The relationship between the the boundary parameters and the two formal parameters appearing in th...