Charging symmetries and linearizing potentials for heterotic string in three dimensions

Abstract

Using the Ernst potential formulation we construct all the finite symmetry transformations which preserve the asymptotics of the bosonic fields of the (dϩ3)-dimensional low-energy heterotic string theory compactified on a d-torus. We combine all the dynamical variables into a single (dϩ1)ϫ(dϩ1ϩn)-dimensional matrix potential which linearly transforms under the action of these symmetry transformations in a transparent SO(2,dϪ1)ϫSO(2,dϪ1ϩn) way, where n is the number of Abelian vector fields. We formulate the most general solution generation technique based on the use of these symmetries and show that they form the invariance group of the general Israel-Wilson-Perjés class of solutions.

String Theory Extensions of Einstein–maxwell Fields: The Static Case

“…In [21] and [20] it was shown that this symmetry coincides with the total group of the three-dimensional charging symmetries of the theory. This group does not affect the trivial spatial asymptotics of the fields and forms the base for the three-dimensional generation technique of asymptotically flat solutions of the theory.…”

“…We consider the toroidal compactification of this theory to three spatial dimensions originally performed in [24]- [25] and settled in a convenient form in [26], [21] and [20]. Let us briefly review some elements of this new formalism which are necessary for the further analysis.…”

“…This analogy, or correspondence, was originally indicated in [21]; its explicit off-and on-shell status was established in [20], whereas some natural applications were given in [27], [28] and [29]. To formulate the correspondence in appropriate terms, let us represent the Einstein-Maxwell theory in a form very similar to the heterotic (bosonic) string theory one (2.2)-(2.3).…”

“…In the pure General Relativity it is impossible to specify the generation procedure in the above mentioned sense because, in fact, there exists only a one-parametric charging symmetry transformation whose 'specification' leads to an identical map. This transformation coincides with the Ehlers symmetry which must be 'normalized' to preserve the asymptotical flatness property, see, for example, [21], where this material together with its straightforward generalization to the string theory case is considered in details. Note that in our approach all the classical nonlinear symmetries (like the Ehlers and Harrison transformations) arise in a matrix-valued framework; nevertheless it is possible to identify some string theory symmetries as the Harrison and Ehlers maps in the conventional non-matrix sense, see [34], [35].…”

Solitons via Lie-Bäcklund transformation for 5D low-energy string theory

“…In this paper we apply a fully parameterized NET [12] on the massless seed solution constructed in [2] in order to get a new solitonic object. In this way we can clarify the physical effect of the NET and make an interpretation of the obtained field configuration.…”