On tensionless strings in 3 + 1 dimensions

We argue for the existence of phase transitions in 3 + 1 dimensions associated with the appearance of tensionless strings. The massless spectrum of this theory does not contain a graviton: it consists of one N = 2 vector multiplet and one linear multiplet, in agreement with the light-cone analysis of the Green-Schwarz string in 3 + 1 dimensions. In M-theory the string decoupled from gravity arises when two 5-branes intersect over a three-dimensional hyperplane. The two 5-branes may be connected by a 2-brane, whose boundary becomes a tensionless string with N = 2 supersymmetry in 3 + 1 dimensions. Non-critical strings on the intersection may also come from dynamical 5-branes intersecting the two 5-branes over a string and wrapped over a 4-torus. The near-extremal entropy of the intersecting 5-branes is explained by the non-critical strings originating from the wrapped 5-branes.