Topology changing processes and symmetries of string effective action

TL;DR

This paper derives wormhole solutions with different topologies from string effective action, highlighting the role of $O(d,d)$ and $SL(2,C)$ symmetries in generating new configurations in string theory.

Contribution

It provides a general method for obtaining wormhole solutions of various topologies from dimensional reduction and explores the use of $SL(2,C)$ and duality symmetries to generate new solutions.

Findings

Wormhole solutions for $R^1\times S^1\times S^2$ and $R^1\times S^3$ geometries are obtained.

The reduced action exhibits a global $SL(2,C)$ symmetry under specific ansatz.

Symmetries are used to generate new internal field configurations leading to wormholes.

Abstract

Wormhole solutions corresponding to space-time geometries $R^1\times S^1\times S^2$ and $R^1\times S^3$ are obtained from reduced string effective action and the action is written in a manifestly $O(d,d)$ invariant form. A general treatment is given for obtaining wormhole solutions of different topologies from dimensional reduction. For specific ansatz of internal metric and antisymmetric field the reduced action is shown to have a global $SL(2,C)$ symmetry. The $SL(2,C)$ and duality symmetries have been exploited to generate new configurations of internal fields which produce wormhole solutions in four space-time dimensions. The $SL(2,C)$ symmetry discussed in this paper arises due to specific form of the moduli and these transformations belong to a subgroup of $O(d,d)$ global symmetry.