  String theory with perimeter action is tensionless by its geometrical nature
and has pure massless spectrum of higher spin gauge particles. I demonstrate
that liner transformation of the world-sheet fields defines a map to the
SO(D,D) sigma model equipped by additional Abelian constraint, which breaks
SO(D,D) to a diagonal SO(1,D-1). The effective tension is equal to the square
of the dimensional coupling constant of the perimeter action. This
correspondence allows to view the perimeter action as a "square root" of the
Nambu-Goto area action. The aforementioned map between tensionless strings and
SO(D,D) sigma model allows to introduce the vertex operators in full analogy
with the standard string theory and to confirm the form of the vertex operators
introduced earlier.
