CLASSICAL AND QUANTIZED TENSIONLESS STRINGS

From the ordinary tensile string we derive a geometric action for the tensionless (T = 0) string and discuss its symmetries and field equati ons. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the T --> 0 limit. We presen t the explicit expressions for the generators of this group in the lig ht-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantu m theory. Modulo details concerning zero-modes that are discussed in t he paper, this leads to the stringent restriction that the physical st ates should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that le ads to this conclusion.