Emergent Spacetime and Holographic CFTs

TL;DR

This paper explores the universal features of holographic conformal field theories, emphasizing the role of operator factorization at large central charge and its connection to AdS fields and the bulk-boundary correspondence.

Contribution

It demonstrates that operator factorization in holographic CFTs occurs only at large central charge and links bootstrap solutions to bulk Witten diagrams, revealing the structure of the holographic dual.

Findings

Factorization holds only in the large central charge limit.

Operators can be represented as fields in AdS, reflecting linearity.

The hologram captures a small sector within a larger Hilbert space.

Abstract

We discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can only hold in the large central charge limit. Using conformal invariance and factorization we argue that these operators are naturally represented as fields in AdS as this makes the underlying linearity of the system manifest. In this class of CFTs the solution of the conformal bootstrap conditions can be naturally organized in structures which coincide with Witten diagrams in the bulk. The large value of the central charge suggests that the theory must include a large number of new operators not captured by the factorized sector. Consequently we may think of the AdS hologram as an effective representation of a small sector of the CFT, which is embedded inside a much larger Hilbert space corresponding to the black hole microstates.