The string theory with perimeter action is tensionless by its geometrical nature and has a pure massless spectrum of higher spin gauge particles. I demonstrate that the linear 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 Nambut-Goto area action. The aforementioned correspondence between tensionless strings and SO(D, D) sigma-model allows to introduce vertex operators in full analogy with the standard string theory and to confirm the form of the vertex operators introduced earlier, the value of the intercept a = 1 and the critical dimension D = 13. (c) 2005 Elsevier B.V. All rights reserved.
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