On the Canonical c-Function in 4-d Field Theories Possessing Supergravity Duals

Abstract

We study monotonicity and other properties of the canonical c-function (defined through the correlator of the energy-momentum tensor) in some holographic duals of 4-d quantum field theories. The canonical c-function and its derivatives are related to the 5-d Green's function of the dual supergravity theory. While positivity of the canonical c-function is obvious, we have not found a general proof of its monotonicity, even though c is monotonic in the few explicit examples we examine in this paper.

12 pages, 4 figures

References in corpus (4)

• The Supergravity Dual of N=1 Super Yang-Mills Theory
• Continuous distributions of D3-branes and gauged supergravity
• A Note on the Holographic Beta and C Functions
• Towards the classification of conformal field theories in arbitrary even dimension

Cited by in corpus (7)

• Holographic Renormalization
• Hypermultiplets, domain walls and supersymmetric attractors
• Correlation Functions in Holographic Renormalization Group Flows
• Exact Consequences of the Trace Anomaly in Four Dimensions
• A Field-theoretical Interpretation of the Holographic Renormalization Group
• CFT/CFT interpolating RG flows and the holographic c-function
• Wilsonian renormalisation and the exact cut-off scale from holographic duality