Ehlers transformations and string effective action

Abstract

We explicitly obtain the generalization of the Ehlers transformation for stationary axisymmetric Einstein equations to string theory. This is accomplished by finding the twist potential corresponding to the moduli fields in the effective two dimensional theory. Twist potential and symmetric moduli are shown to transform under an O(d, d) which is a manifest symmetry of the equations of motion. The non-trivial action of this O(d, d) is given by the Ehlers transformation and belongs to the set O(d)×O(d) O(d) .

Inverse scattering method and soliton double solution family for string effective action

“…For later use, here we briefly recall some related concepts and notations of the ED-complex function [30] and equations of motion for the EDKR theory [5,7,8].…”

“…For the heterotic string = 8, but we keep arbitrary in the present discussion. Following Maharana and Schwarz [1] and Sen [28,29], when dimensionally reducing the above theory from 2 + to 2 dimensions by compactification on a -dim torus, (3) can be reduced to the following effective action [5,7,8] …”

“…[1][2][3][4][5][6][7][8][9][10] (the so-called Einstein-dilaton-KalbRamond (EDKR) theory) is a typical and very important model of this kind. Some analogies between the EDKR theory and the reduced vacuum Einstein theory have been noted.…”

“…The difficulties have to do with the complicated mathematical structures, such as the fundamental field matrices in the reduced string effective theories in general have dimensions greater than two and, at the same time, must satisfy some non-trivial Riemannian symmetric space (or coset) conditions [1,28,29], etc. (For example, the fundamental field matrix of the EDKR theory considered in this paper belongs to the symmetric [5,7,8].) Therefore, it would be worth while to develop some more effective ISM and obtain more general new exact (soliton) solutions of the string effective theories.…”

“…In Section 2, some related concepts and notations of the ED-complex function [30] and the equations of motion [5,7,8] for the EDKR theory are briefly recalled. In Section 3, the EDKR equations are extended to an ED formulation and a modified HE-type ED-complex linear system for the EDKR theory is established.…”