Two dimensional RG flows and Yang-Mills instantons

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 × 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) ⋉ 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.