Higher-Spin Gauge Interactions for Matter Fields in Two Dimensions

We formulate a new model which describes higher-spin gauge interactions for matter fields in two dimensions. This model is a higher-spin generalization of d2 gravity and turns out to be integrable. No vanishing higher-spin current conditions are imposed on the matter fields.Comment: LaTex, 10 pages, no figures, to be published in Phys. Lett.

Physical States in G/G Models and 2d Gravity

An analysis of the BRST cohomology of the G/G topological models is performed for the case of $A_1^{(1)}$. Invoking a special free field parametrization of the various currents, the cohomology on the corresponding Fock space is extracted. We employ the singular vector structure and fusion rules to translate the latter into the cohomology on the space of irreducible representations. Using the physical states we calculate the characters and partition function, and verify the index interpretation. We twist the energy-momentum tensor to establish an intriguing correspondence between the ${SL(2)\over SL(2)}$ model with level $k={p\over q}-2$ and $(p,q)$ models coupled to gravity.Comment: 42 page