Gravity from CFT on $S^N(X)$ CFT: Symmetries and Interactions

TL;DR

This paper explores the algebraic structure and dynamics of an orbifold CFT dual to string theory on $ADS_3 imes S^3$, revealing new features related to stringy exclusion and black holes through collective field techniques.

Contribution

It introduces a Lie algebra from chiral primaries that determines the theory's dynamics and uncovers novel features linked to thresholds and non-commutative spacetime.

Findings

Derived algebraic structures from correlation functions.

Identified thresholds related to stringy exclusion principle and black holes.

Connected fusion rules to non-commutative spacetime evidence.

Abstract

The orbifold CFT dual to string theory on $ADS_3 \times S^3$ 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^{i \pi / {N+1}} $, and the correlation functions, which provide further evidence for a non-commutative spacetime.