Rotating string in doubled geometry with generalized isometries

TL;DR

This paper constructs a non-geometric background with branes in type II string theory, demonstrates axisymmetry in doubled geometry, and shows conserved charges for a rotating string solution within this framework.

Contribution

It introduces a globally well-defined non-geometric background with branes and reveals generalized isometries allowing conserved charges for rotating strings.

Findings

Constructed a non-geometric background with 5^2_2-branes.

Identified generalized Killing vectors in doubled geometry.

Proved charge conservation for rotating strings in non-geometric backgrounds.

Abstract

In this paper, we first construct a globally well-defined non-geometric background which contains several branes in type II string theory compactified on a 7-torus. One of these branes is called 5^2_2, which is a codimension-2 object and has a non-trivial monodromy given by a T-duality transformation. The geometry near the 5^2_2-brane is shown to approach the non-geometric background constructed in arXiv:1004.2521. We then construct the solution of a fundamental string rotating along a non-trivial cycle in the 5^2_2 background. Although the background is not axisymmetric in the usual sense, we show that it is actually axisymmetric as a doubled geometry by explicitly finding a generalized Killing vector. We perform a generalized coordinate transformation into a system where the generalized isometry is manifest, and show that the winding and momentum charges of the string solution is explicitly conserved in that system.