  Starting from the Polyakov action we consider two distinct Carroll limits in
target space, keeping the string worldsheet relativistic. The resulting
magnetic and chiral Carroll string models exhibit different symmetries and
dynamics. Both models have an infinite dimensional symmetry algebra with
Carroll symmetry included in a finite dimensional subalgebra. For the magnetic
model, this is the so-called string Carroll algebra. The chiral model realises
an extended version of the string Carroll algebra. The magnetic model does not
have any transverse string excitations. The chiral model is less restrictive
and includes arbitrary left-moving modes that carry transverse momentum but do
not contribute to the energy in target space.
