  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.
