The quantization of a free boson whose momentum satisfies a cubic constraint leads to a c= conformal field theory with a BRST symmetry. The theory also has a W_∞ symmetry in which all the generators except the stress-tensor are BRST-exact and so topological. The BRST cohomology includes states of conformal dimensions 0", together with copies' of these states obtained by acting with picture-changing and screening operators. The 3-point and 4-point correlation functions agree with those of the

more »

... ng model, suggesting that the theory is equivalent to the critical Ising model. At tree level, the W_3 string can be viewed as an ordinary c=26 string whose conformal matter sector includes this realisation of the Ising model. The two-boson W_3 string is equivalent to the Ising model coupled to two-dimensional quantum gravity. Similar results apply for other W-strings and minimal models.