arXiv subjects
Publications and source records attributed to A. A. Kapustnikov.
It is shown that the method of nonlinear realization of local supersymmetry being applied to the n=(1,1) superconformal symmetry allows one reduce the new version of the super-Liouville equation to the ordinary one owing to the relaxation of the auxiliary equation of motion fixing the gauge parameters.
It is shown that the method of the nonlinear realization of local supersymmetry previously developed in framework of supergravity being applied to the n=(2,2) superconformal symmetry allows one to get the new form of the exactly solvable n=(2,2) super-Liouville equation. The general advantage of this version as compared with the conventional one is that its bosonic part includes the complex Liouville equation. We obtain the suitable supercovariant constraints imposed on the corresponding superfields which provide the set of the resulting system of component equations be the same as that in model of N=2, D=4 Green-Schwarz superstring. The general solution of this system is derived from the corresponding solution of the bosonic string equation.
The new principle of constrained twistor-like variables is proposed for construction of the Cartan 1-forms on the worldsheet of the D=3,4,6 bosonic strings. The corresponding equations of motion are derived. Among them there are two well-known Liouville equations for real and complex worldsheet functions W(s,\bar s). The third one in which W(s,\bar s) is replaced by the quaternionic worldsheet function is unknown and can be thought of as that of the SU(2) nonlinear sigma-model governing the classical dynamics of the bosonic string in D=6.
A new approach to the quantization of the relativistic kink - model around the solitonic solution is developed on the ground of the collective coordinates method. The corresponding effective action is proved to be the action of the nonminimal $d=1+1$ point - particle with curvature. It is shown that upon canonical quantization this action yields the spectrum of kink - solution obtained firstly with the help of the WKB - quantization.