Gravity from CFT on SN(X) : symmetries and interactions Original Research Article

The orbifold CFT dual to string theory on AdS3×S3 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 L0=N , L0=N/2 and L0=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=eiπ/(N+1) , and the correlation functions, which provide further evidence for a non-commutative spacetime.