AdS/CFT and local renormalization group with gauge fields

Understand

We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence.

• Starting with a $(d+1)$-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory.
• The Gauss's law constraint associated with gauge symmetry plays an important role.
• RG flows of the background gauge fields are governed by vector $\beta$-functions, and some interesting properties of them are known to follow.