Wilsonian renormalisation and the exact cut-off scale from holographic duality

Understand

We propose a method for determining the exact correspondence between the Wilsonian cut-off scale on the boundary and its holographically dual bulk theory.

• We systematically construct the multi-trace Wilsonian effective action from holographic renormalisation and evolve it by integrating out the asymptotically Anti-de Sitter bulk geometry with scalar probes.
• The Wilsonian nature of the effective action is shown by proving that it must be either double-trace, closing in on itself under successive integrations, or have an infinite series of multi-trace terms.
• Focusing on composite scalar operator renormalisation, we relate the Callan-Symanzik equation, the flow of the scalar anomalous dimension and the multi-trace beta functions to their dual RG flows in the bulk.