Universality of Long-Distance AdS Physics from the CFT Bootstrap (1403.6829v2)

Abstract: We begin by explicating a recent proof of the cluster decomposition principle in AdS_{d+1} from the CFT_d bootstrap in d > 2. The CFT argument also computes the leading interactions between distant objects in AdS, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit. We proceed to study the generalization to 2d CFTs, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the 2d bootstrap we prove the existence of large spin operators with fixed 'anomalous dimensions' indicative of the presence of deficit angles in AdS_3. As we approach the threshold for the BTZ black hole, interpreted as a CFT scaling dimension, the twist spectrum of large spin operators becomes dense. Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasi-normal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.

• The paper proves that long-distance AdS interactions are universally captured via the CFT bootstrap, confirming a key aspect of holographic duality.
• It employs cluster decomposition and semiclassical calculations of Virasoro blocks to derive non-perturbative insights into gravitational interactions in AdS space.
• Findings imply that specific CFT operators govern both thermalization phenomena and gravitational forces, bridging quantum gravity with classical spacetime dynamics.

Universality of Long-Distance AdS Physics from the CFT Bootstrap

The paper "Universality of Long-Distance AdS Physics from the CFT Bootstrap" investigates the intricate relationship between Anti-de Sitter (AdS) spacetime physics and conformal field theory (CFT) using the bootstrap approach. The authors aim to demonstrate that AdS physics, particularly long-distance interactions, can be described by the universal features of CFT, specifically focusing on the implications of the bootstrap process and its application across various dimensions.

Overview and Key Findings

The central focus of the paper is to establish that the bootstrap approach in CFT can be used to explain long-distance physics in AdS spacetimes. This link contributes to our understanding of the AdS/CFT correspondence, a cornerstone of modern theoretical physics, which posits a duality between theories of gravity in AdS space and CFTs.

1. Cluster Decomposition in AdS:
   • The authors prove the cluster decomposition principle for AdS$_{d+1}$ spaces, inferred from CFT$_d$ bootstrap for $d \geq 3$. This principle pertains to the factorization of dynamics into independent local events at large distances, crucial for understanding locality in AdS.
2. CFT$_2$ Extension:
   • Extending the paper to two-dimensional CFTs (CFT$_2$), the authors explore the role of Virasoro conformal blocks in a lightcone Operator Product Expansion (OPE) limit. They calculate these blocks within a semiclassical, large central charge framework, revealing insights into the operator structure in AdS$_3$.
3. Gravitational and Gauge Forces:
   • The paper confirms that the leading interactions between distant objects in AdS are universally reflected in the CFT and can be computed in the semiclassical limit. This leads to predictions regarding gravitational forces in AdS interpreted through the CFT lens.
4. Virasoro Blocks and BTZ Black Holes:
   • By examining the Virasoro identity block, the authors deduce that states above a certain dimensional threshold mimic a thermal background for light operators due to the exchange of Virasoro identity blocks. This finding relates to the thermodynamics of the BTZ black hole environment and the spectrum of its quasi-normal modes.
5. Spectral Density and Entanglement:
   • In the context of CFT$_2$, the paper examines the dense spectrum of large spin operators approaching the BTZ threshold, illustrating how eigenstate thermalization occurs.

Implications and Future Directions

The paper deepens our understanding of AdS/CFT correspondence, elucidating how long-distance effects in AdS arise naturally from CFTs. This work presents a non-perturbative perspective on gravitational interactions in AdS spacetimes reflected in the universal structure of CFTs.

• Theoretical Implications:
  • The results support the notion that gravity in AdS spaces and thermodynamics in higher dimensions can be emergently described via CFT dynamics. It identifies specific operators in CFT responsible for gravitational interactions, contributing to the foundational understanding of holography.
• Practical Implications:
  • Practically, this investigation could influence how physicists model and simulate interactions in quantum gravity and high-energy physics, providing a framework that bridges holographic theories with observable physical phenomena.
• Future Prospects:
  • Future studies might focus on refining the understanding of thermalization processes in holographic systems and extending the bootstrap method to more complex symmetries and interactions in AdS/CFT setups.

This paper significantly contributes to the field of quantum gravity and string theory by consolidating a fundamental connection between macroscopic AdS interactions and their microscopic origins in CFT, a critical step towards unraveling the nature of spacetime at quantum scales.