The orbifold CFT dual to string theory on ADS 3 ×S 3 allows a construction of gravitational actions based on collective field techniques. We describe a fundamental role played by a Lie algebra constructed from chiral primaries and their CFT conjugates. The leading terms in the algebra at large N are derived from the computation of chiral primary correlation functions. The algebra is argued to determine the dynamics of the theory, its representations provide free and interacting hamiltonians for chiral primaries. This dynamics is seen to be given by an effective one plus one dimensional field theory. The structure of the algebra and its representations shows qualitatively new features associated with thresholds at L 0 = N , L 0 = N/2 and L 0 = N/4, which are related to the stringy exclusion principle and to black holes. We observe relations between fusion rules of SU q (2|1, 1) for q = e iπ N +1 , and the correlation functions, which provide further evidence for a non-commutative spacetime. 11/98

In the framework of the conjectured duality relation between large N gauge theory and supergravity the spectra of masses in large N gauge theory can be determined by solving certain eigenvalue problems in supergravity. In this paper we study the eigenmass problem given by Witten as a possible approximation for masses in QCD without supersymmetry. We place a particular emphasis on the treatment of the horizon and related boundary conditions. We construct exact expressions for the analytic expansions of the wave functions both at the horizon and at infinity and show that requiring smoothness at the horizon and normalizability gives a well defined eigenvalue problem. We show for example that there are no smooth solutions with vanishing derivative at the horizon. The mass eigenvalues up to m 2 = 1000 corresponding to smooth normalizable wave functions are presented. We comment on the relation of our work with the results found in a recent paper by Csáki et al., hep-th/9806021, which addresses the same problem.

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