Gravity from CFT on S-N(X): symmetries and interactions

The orbifold CFT dual to string theory on AdS(3) x S-3 allows a constructio n of gravitational actions based on collective field techniques. We describ e a fundamental role played by a Lie algebra constructed from chiral primar ies and their CFT conjugates. The leading terms in the algebra at large N a re derived from the computation of chiral primary correlation functions. Th e algebra is argued to determine the dynamics of the theory, its representa tions 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 qualita tively 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 SUq (2\1, 1) for q = e( i pi/(N+1)), and the correlation functions, which provide further evidence for a non-commutative spacetime. (C) 2000 Elsevier Science B.V. All rights reserved.