Tensionless strings, correspondence with SO(D,D) sigma-model

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 Nambu-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.