An Exact Holographic RG Flow Between 2d Conformal Fixed Points
Marcus Berg, Henning Samtleben
TL;DR
The paper presents an exact holographic RG flow between two-dimensional conformal fixed points realized as a domain wall in 3D gauged supergravity with gauge group $SO(4)\times SO(4)$. The UV point is an $N=(4,4)$ SCFT linked to the double D1-D5 system, deformed by a relevant operator of dimension $\Delta=\tfrac{3}{2}$ to an IR $N=(1,1)$ fixed point with $c_{\rm IR}/c_{\rm UV}=\tfrac{1}{2}$. The authors construct an analytic kink solution, compute holographic counterterms and one-point functions for inert scalars, and derive fluctuation equations that reduce to two universal second-order ODEs for inert scalars and vector-longitudinal modes, enabling the eventual extraction of two-point functions along the flow. This exact flow serves as a tractable toy model for conformal-to-conformal flows in higher dimensions and provides insights into the structure of correlation functions in strongly coupled two-dimensional theories.
Abstract
We describe a supersymmetric RG flow between conformal fixed points of a two-dimensional quantum field theory as an analytic domain wall solution of the three-dimensional SO(4) x SO(4) gauged supergravity. Its ultraviolet fixed point is an N=(4,4) superconformal field theory related, through the double D1-D5 system, to theories modeling the statistical mechanics of black holes. The flow is driven by a relevant operator of conformal dimension Δ=3/2 which breaks conformal symmetry and breaks supersymmetry down to N=(1,1), and sends the theory to an infrared conformal fixed point with half the central charge. Using the supergravity description, we compute counterterms, one-point functions and fluctuation equations for inert scalars and vector fields, providing the complete framework to compute two-point correlation functions of the corresponding operators throughout the flow in the two-dimensional quantum field theory. This produces a toy model for flows of N=4 super Yang-Mills theory in 3+1 dimensions, where conformal-to-conformal flows have resisted analytical solution.