14536317
Solutions of conformal turbulence on a half plane
Abstract Exact solutions of conformal turbulence restricted to the upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tuning of coefficients. The simplest solution in our case is given by the minimal model of p = 2, q = 33 and moreover we find a fixed point of solutions when p , q become large.
15532318
Deformed minimal models and generalized Toda theory
Abstract We introduce a generalization of A r -type Toda theory based on a non-Abelian group G , which we call the ( A r , G )-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine ( A 1 , SU (2))-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator Φ (2,1) . We derive infinite conserved charges and soliton solutions from the Lax pair of the affine ( A 1 , SU (2))-Toda theory. Another type of integrable deformation which accounts for the Φ (3,1) -deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.
15330171
Classical matrix sine-Gordon theory
Abstract The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3 generalization where fields take values in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2) × SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explaining their physical properties. Infinite current conservation laws and then Backlund transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the Backlund transformation, we also derive exact solutions as well as a nonlinear superposition principle by making use of Bianchi's permutability theorem.
15297893
Possible tests of conformal turbulence through boundaries
Abstract We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum E ( k ) or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter q appears explicitly in the one point functions in the theory, which can also be tested.
15611022
Complex sine-Gordon Theory for Coherent Optical Pulse Propagation
It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.
122640782
D3 + D6 solution and D4 + D6 solution
Abstract We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D =11 solutions (M3 branes and M4 branes with the Z N identifications in the transverse space) we obtain the D =10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D =10 along a circular direction of S 3 part of the transverse space. M3 brane solution leads to D =10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.