An Exact Holographic RG Flow Between 2d Conformal Fixed Points

TL;DR

This paper constructs an exact supersymmetric holographic RG flow between two 2D conformal fixed points using supergravity, providing a detailed framework for calculating correlation functions and modeling complex quantum field theory flows.

Contribution

It presents an analytic domain wall solution describing a supersymmetric RG flow between 2D conformal fixed points, including detailed calculations of correlation functions in the supergravity framework.

Findings

Identified a specific RG flow driven by a relevant operator with /2 dimension.

Computed counterterms, one-point functions, and fluctuation equations for the flow.

Provided a toy model for complex conformal flows in higher-dimensional super Yang-Mills 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 \Delta=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.