forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2650
Articles: 1'968'170
Articles rated: 2572

06 July 2020
  » 1718870

  Article forum

Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
G. A. Alekseev ;
Date 29 May 2012
AbstractThe monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for gravity coupled bosonic dynamics in string gravity and supergravity in four and higher dimensions. For different types of fields in space-times of $Dge 4$ dimensions with $d=D-2$ commuting isometries -- stationary fields with spatial symmetries, interacting waves or partially inhomogeneous cosmological models, the string gravity equations govern the dynamics of interacting gravitational, dilaton, antisymmetric tensor and any number $nge 0$ of Abelian vector gauge fields (all depending only on two coordinates). The equivalent spectral problem constructed earlier allows to parameterize the infinite-dimensional space of local solutions of these equations by two pairs of cal{arbitrary} coordinate-independent holomorphic $d imes d$- and $d imes n$- matrix functions ${mathbf{u}_pm(w), mathbf{v}_pm(w)}$ of a spectral parameter $w$ which constitute a complete set of monodromy data for normalized fundamental solution of this spectral problem. The "direct" and "inverse" problems of such monodromy transform --- calculating the monodromy data for any local solution and constructing the field configurations for any chosen monodromy data always admit unique solutions. We construct the linear singular integral equations which solve the inverse problem. For any emph{rational} and emph{analytically matched} (i.e. $mathbf{u}_+(w)equivmathbf{u}_-(w)$ and $mathbf{v}_+(w)equivmathbf{v}_-(w)$) monodromy data the solution for string gravity equations can be found explicitly. Simple reductions of the space of monodromy data leads to the similar constructions for solving of other integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or vacuum gravity in $Dge 4$ dimensions.
Source arXiv, 1205.6238
Services Forum | Review | PDF | Favorites   

No message found in this article forum.  You have a question or message about this article? Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..

Subject of your forum message:
Write your forum message below (min 50, max 2000 characters)

2000 characters left.
Please, read carefully your message since you cannot modify it after submitting.

  To add a message in the forum, you need to login or register first. (free): registration page
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica