Seeing a c-theorem with holography (1006.1263v2)

Abstract: There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms. The latter allows us to distinguish the flow of the central charges $a$ and $c$ in the dual field theories in four dimensions. One finds that the flow of $a$ is naturally monotonic but that of $c$ is not. Extending the analysis of holographic RG flows to higher dimensions, we are led to formulate a novel c-theorem in arbitrary dimensions for a universal coefficient appearing in the entanglement entropy of the fixed point CFT's.

• The paper introduces a generalized c-theorem that extends Cardy’s conjecture to higher dimensions via holographic RG flows.
• It employs higher-curvature gravity models to differentiate the behavior of central charges a and c in four-dimensional CFTs.
• It links a universal entanglement entropy coefficient with RG flow dynamics, indicating a consistent monotonic decrease from UV to IR.

Overview of "Seeing a c-theorem with holography"

The paper "Seeing a c-theorem with holography" by Myers and Sinha investigates the possibility of extending the c-theorem, a fundamental result in two-dimensional quantum field theory (QFT), to higher dimensions using holographic principles. The authors employ a holographic model of renormalization group (RG) flows within a bulk gravity theory that incorporates higher curvature terms, allowing for the distinction between different central charges in four-dimensional conformal field theories (CFTs).

Key Contributions

The main contribution of this work is the proposed extension of the c-theorem to arbitrary dimensions by considering holographic RG flows. The paper examines how central charges, notably the coefficients $a$ and $c$, behave under these flows and provides a framework to understand their evolution. Central to their analysis is the construction of a higher curvature gravity model that differentiates the flow of these charges, showing that $a$ tends to flow monotonically, while $c$ does not necessarily do so.

Additionally, the authors propose a novel c-theorem applicable to arbitrary dimensions, linking it to a universal coefficient in the entanglement entropy of fixed-point CFTs. They conjecture that this coefficient should decrease in any RG flow from a UV to an IR fixed point.

Methodology

The authors construct their analysis within the AdS/CFT correspondence framework, a well-established theoretical approach that relates a gravitational theory in an Anti-de Sitter (AdS) space to a conformal field theory on the boundary of that space. They employ actions that include higher curvature terms, such as quasi-topological gravity, allowing for exploration of RG flows that are sensitive to different central charge dynamics.

• Higher Curvature Theories: By considering gravity theories with higher curvature interactions, the authors are able to distinguish between central charges $a$ and $c$ in four-dimensional CFTs. This differentiation is crucial for examining the conjectured c-theorem in these contexts.
• Holographic RG Flows: They use holographic methods to derive flow functions and demonstrate monotonic behavior of these functions under RG flows.

Significant Results

The paper provides evidence supporting the irreversibility of the RG flow for the central charge $a$, reinforcing Cardy’s conjecture for four-dimensional CFTs and extending its relevance to higher dimensions. The findings suggest that a certain universal term in the entanglement entropy, associated with this central charge, adheres to a monotonically decreasing behavior from the UV to the IR fixed points.

Implications and Future Directions

The theoretical implications of this research lie primarily in its potential to inform the development of a generalized c-theorem for CFTs in various dimensions, both even and odd. By linking pivotal properties of the entanglement entropy to RG flow dynamics, the work also suggests new insights into the nature of entanglement in quantum field theories.

The practical implications could extend to any computational or analytical contexts where understanding the non-trivial behavior of quantum field theories under RG transformations is critical.

For future work, the authors anticipate further investigation into more explicit demonstrations and potential generalizations of their conjecture beyond a holographic framework. This could include deriving the holographic entanglement entropy relation in more general settings and examining its implications for CFTs that do not necessarily adhere to the constraints of holographic duality.

In summary, this paper provides a substantial theoretical advancement in understanding RG flows via holographic methods, presenting a robust conjecture for a generalized c-theorem applicable to higher dimensions.