Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories

The equation of motion of affine Toda field theory is a coupled equation for $r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theories admit reduction, in which the equation is satisfied by fewer than $r$ fields. The reductions in the existing literature are achieved by identifying (folding) the points in the Dynkin diagrams which are connected by symmetry (automorphism). In this paper we present many new reductions. In other words the symmetry of affine Dynkin diagrams could be extended and it leads to non-canonical foldings. We investigate these reductions in detail and formulate general rules for possible reductions. We will show that eventually most of the theories end up in $a_{2n}^{(2)}$ that is the theory cannot have a further dimension $m$ reduction where $m<n$.Comment: 26 pages, Latex2e, usepackage `graphics.sty', 15 figure

Symmetries of String Effective Action and Space-Time Geometry

Two dimensional charged black hole solution is obtained by implementing an $O(2,2)$ transformation on the three dimensional black string solution. Two different monopole backgrounds in five dimensions are related through an $O(2,2)$ transformation. It has been shown in these examples that the particular $O(2,2)$ transformation corresponds to duality transformation.Comment: 14 page

String Effective Action and Two Dimensional Charged Black Hole

Graviton-dilaton background field equations in three space-time dimensions, following from the string effective action are solved when the metric has only time dependence. By taking one of the two space dimensions as compact, our solution reproduces a recently discovered charged black hole solution in two space-time dimensions. Solutions in presence of nonvanishing three dimensional background antisymmetric tensor field are also discussed.Comment: 11 page

Instability of Solitons in imaginary coupling affine Toda Field Theory

Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable properties, such as real total energy/momentum and mass. Several authors calculated quantum mass corrections of the solitons by claiming these solitons are stable. We show that there exists a large class of classical solutions which develops singularity after a finite lapse of time. Stability claims, in earlier literature, were made ignoring these solutions. Therefore we believe that a formulation of quantum theory on a firmer basis is necessary in general and for the quantum mass corrections of solitons, in particular.Comment: 17 pages, latex, no figure

Affine Toda field theory from tree unitarity

Elasticity property (i.e. no-particle creation) is used in the tree level scattering of scalar particles in 1+1 dimensions to construct the affine Toda field theory(ATFT) associated with root systems of groups $a_2^{(2)}$ and $c_2^{(1)}$. A general prescription is given for constructing ATFT (associated with rank two root systems) with two self conjugate scalar fields. It is conjectured that the same method could be used to obtain the other ATFT associated with higher rank root systems.Comment: 22 pages, 50 postscript figure files, Latex2e Added reference, typos corrected, minor text modificatio

S-matrices of non-simply laced affine Toda theories by folding

The exact factorisable quantum S-matrices are known for simply laced as well as non-simply laced affine Toda field theories. Non-simply laced theories are obtained from the affine Toda theories based on simply laced algebras by folding the corresponding Dynkin diagrams. The same process, called classical `reduction', provides solutions of a non-simply laced theory from the classical solutions with special symmetries of the parent simply laced theory. In the present note we shall elevate the idea of folding and classical reduction to the quantum level. To support our views we have made some interesting observations for S-matrices of non-simply laced theories and give prescription for obtaining them through the folding of simply laced ones.Comment: 26 pages, Latex2e, 4 figure

The Effect of w−termw-term on Visibility Correlation and Power Spectrum Estimation

Visibility-visibility correlation has been proposed as a technique for the estimation of power spectrum, and used extensively for small field of view observations, where the effect of $w-term$ is usually ignored. We consider power spectrum estimation from the large field of view observations, where the $w-term$ can have a significant effect. Our investigation shows that a nonzero $w$ manifests itself as a modification of the primary aperture function of the instrument. Using a gaussian primary beam, we show that the modified aperture is an oscillating function with a gaussian envelope. We show that the two visibility correlation reproduces the power spectrum beyond a certain baseline given by the width, $U_{w}$ of the modified aperture. Further, for a given interferometer, the maximum $U_{w}$ remains independent of the frequencies of observation. This suggests that, the incorporation of large field of view in radio interferometric observation has a greater effect for larger observing wavelengths.Comment: 9 pages, 4 figures, 2 table