Universal Bound on Effective Central Charge and Its Saturation (2404.01515v2)

Abstract: The effective central charge (denoted by $c_{\text{eff}}$) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient $c_{LR}$ of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this article, we propose the inequalities, $0 \leq c_{LR} \leq c_{\text{eff}} \leq \min (c_L,c_R)$. They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.

• The paper establishes a universal inequality where energy transmission does not exceed information transfer across conformal interfaces.
• It validates the proposed bound using AdS/CFT correspondence, free field theories, and defect perturbation techniques.
• Saturation conditions highlight critical links between entanglement metrics and thermal dynamics in various conformal field theory frameworks.

Universal Bound on Effective Central Charge and Its Saturation

The paper, "Universal Bound on Effective Central Charge and Its Saturation," presents an analysis of the relationship between energy and information transmission across conformal interfaces within the context of conformal field theory (CFT), particularly leveraging insights from the AdS/CFT correspondence. The paper enhances understanding by introducing an inequality and proving its validity through various theoretical frameworks, including holographic CFTs, free CFTs, and defect perturbation theory. This work posits a set of inequalities that govern the effective central charge $(c_{\text{eff}})$ and the transmission coefficient $(c_{LR})$, characterized by the relation $$0 \leq c_{LR} \leq c_{\text{eff}} \leq \min(c_L, c_R)$$.

Principal Insights

The paper begins by outlining the crucial roles played by conformal interfaces in interfacing different quantum critical systems. These interfaces are characterized by sometimes opposing measures: the effective central charge, indicative of entanglement across the interface, and the transmission coefficient, which characterizes energy transfer. The authors establish the conjecture that energy transmission cannot exceed information transmission, encapsulated in the inequality $c_{LR} \leq c_{\text{eff}}$. This conjecture holds potential implications for understanding quantum information flow and thermal properties in CFTs.

Verification of the inequality is achieved through several methodologies:

1. Holographic CFTs: The application of AdS/CFT correspondence provides a robust foundation for confirming the proposed bounds and understanding conditions under which they are saturated.
2. Free Field Examples: The work extends beyond holography, showing the applicability of the inequality within free field theories.
3. Defect Perturbation Theory: The perturbative approach to interfaces within defect CFTs supports the conjecture, indicating that energy transmission is inherently limited by intertwining entropic considerations.

Saturation and Generality

Further examination reveals that the inequality $c_{LR} = c_{\text{eff}}$ is saturated in specific conditions. Interfaces that achieve this include cases where $c_{\text{eff}}$ equals either the minimal central charge of the two coupled CFTs, suggesting interfaces that are either at topological limits or exhibit boundary characteristics manifesting zero energy or information transmission.

Theoretical Implications

This investigation into the balance of entanglement and energy transmission involves potentially profound implications in theoretical contexts:

• Extension of Holographic Dualities: By delineating conditions for inequality saturation, potential pathways for exploring other models of holography in non-boundary configurations or higher-dimensional CFTs are opened.
• Understanding Non-topological Interfaces: The research lays the groundwork for distinguishing between topological and more intricate non-topological interfaces in terms of their energetic and informational dynamics.

Future Directions

The findings of this paper inspire several further research directions:

• Mathematical Proofs for General CFTs: There is a need for establishing the bounds beyond the domain of holographic and perturbation theory approximations.
• Numerical Simulations: Lattice simulations could be employed to explore the theoretical predictions in more diversified CFT models.
• Higher-dimensional Analogues: Given the universality attributed to the observed phenomena, extending these results to CFTs of higher dimensions could reveal more about the ubiquitous nature of these entropic and transmission bounds.

The research represents a step forward in understanding the fundamental limits of quantum information fragmentation and flow in theoretical physics, potentially influencing both conceptual foundations and practical computations in quantum field theories. Such endeavors hold importance for both expanding the theoretical framework of CFTs and for potential applications in quantum computing and information science.