New discrete states in two-dimensional supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the super-conformal beta-gamma ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU(N) multiplets if the algebra includes the currents of ghost numbers n : -N <= n <= N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU(3) Clebsch-Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.