Abstract
We revisit the fundamental string (F1) solution in the doubled formalism. We show that the wave-like solution of double field theory (DFT) corresponding to the F1/pp-wave duality pair is more properly a solution of the DFT action coupled to a doubled sigma model action. The doubled string configuration which sources the pp-wave can be thought of as static gauge with the string oriented in a dual direction. We also discuss the DFT solution corresponding to a vibrating string, carrying both winding and momentum. We further show that the solution dual to the F1 in both time and space can be viewed as a "negative string" solution. Negative branes are closely connected to certain exotic string theories which involve unusual signatures for both spacetime and brane worldvolumes. In order to better understand this from the doubled point of view, we construct a variant of DFT suitable for describing theories in which the fundamental string has a Euclidean worldsheet, for which T-dualities appear to change the spacetime signature.
Highlights
The goal of so-called “doubled formalisms” is to pair the string coordinates with their T-duals in order to achieve duality invariance as a manifest symmetry
We show that the wave-like solution of double field theory (DFT) corresponding to the F1/ppwave duality pair is more properly a solution of the DFT action coupled to a doubled sigma model action
In order to better understand this from the doubled point of view, we construct a variant of DFT suitable for describing theories in which the fundamental string has a Euclidean worldsheet, for which T-dualities appear to change the spacetime signature
Summary
The goal of so-called “doubled formalisms” is to pair the string coordinates with their T-duals in order to achieve duality invariance as a manifest symmetry This has been pioneered in particular by [1,2,3,4,5,6,7], leading to doubled worldsheet actions, and has been applied to supergravity to give double field theory (DFT) [4, 5, 8,9,10,11]. This is called a choice of “section” If this doubled wave is oriented, the solution reduces in spacetime to that of the pp-wave, while if instead it is oriented in a dual direction the solution appears as a string. The two appendices give additional results related to the doubled worldsheet (in appendix A) and to DFT (in appendix B)
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