Holographic RG Flow on the Defect and g-Theorem

TL;DR

This paper explores the holographic description of RG flows in defect conformal field theories, proposing a g-function that decreases monotonically along the flow, and verifies this in a D5-brane solution related to mass deformation.

Contribution

It introduces a holographic g-function for defect CFTs and proves the g-theorem, demonstrating its monotonicity in a specific D5-brane solution.

Findings

The g-function is monotonically non-increasing along the RG flow.

The proposed g-theorem is validated in the D5-brane solution.

The study connects holographic RG flow with defect CFT deformations.

Abstract

We investigate relevant deformation and the renormalization group flow in a defect conformal field theory from the point of view of the holography. We propose a candidate of g-function in the context of the holography, and prove the g-theorem: the g-function is monotonically non-increasing along the RG flow. We apply this g-theorem to the D5-brane solution which is an asymptotically AdS_4 x S^2 brane in AdS_5 x S^5. This solution corresponds to the mass deformation of the defect CFT. We checked that the g-function is monotonically non-increasing in this solution.