Two dimensional RG flows and Yang-Mills instantons

TL;DR

This paper investigates RG flow solutions in six-dimensional supergravity with Yang-Mills instantons, revealing interpolations between supersymmetric AdS3 backgrounds and their dual 2D SCFT interpretations, including a reduction to three dimensions.

Contribution

It presents new RG flow solutions involving Yang-Mills instantons in 6D supergravity, with a detailed analysis of their dual 2D SCFTs and a consistent 3D reduction for the SU(2) case.

Findings

Interpolating solutions between two AdS3 backgrounds with different radii.

Explicit reduction ansatz for the SU(2) instanton case to three dimensions.

Interpretation of flows as vacuum expectation value deformations in dual SCFTs.

Abstract

We study RG flow solutions in (1,0) six dimensional supergravity coupled to an anti-symmetric tensor and Yang-Mills multiplets corresponding to a semisimple group $G$. We turn on $G$ instanton gauge fields, with instanton number $N$, in the conformally flat part of the 6D metric. The solution interpolates between two (4,0) supersymmetric $AdS_3\times S^3$ backgrounds with two different values of $AdS_3$ and $S^3$ radii and describes an RG flow in the dual 2D SCFT. For the single instanton case and $G=SU(2)$, there exist a consistent reduction ansatz to three dimensions, and the solution in this case can be interpreted as an uplifted 3D solution. Correspondingly, we present the solution in the framework of N=4 $(SU(2)\ltimes \mathbf{R}^3)^2$ three dimensional gauged supergravity. The flows studied here are of v.e.v. type, driven by a vacuum expectation value of a (not exactly) marginal operator of dimension two in the UV. We give an interpretation of the supergravity solution in terms of the D1/D5 system in type I string theory on K3, whose effective field theory is expected to flow to a (4,0) SCFT in the infrared.