Gravitational and Yang-Mills instantons in holographic RG flows

We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of AN − 1 type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_3} \times {S^3}}} \left/ {{{\mathbb{Z}_N}}} \right.} $\end{document} and AdS3 × S3 geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by a vacuum expectation value of a marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I′ context. In type IIB theory, the flow interpolates between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_5} \times {S^5}}} \left/ {{{\mathbb{Z}_N}}} \right.} $\end{document} and AdS5 × S5 geometries. The field theory interpretation is that of an N = 2 SU(n)N quiver gauge theory flowing to N = 4 SU(n) gauge theory. In type I′ theory the solution describes an RG flow from N = 2 quiver gauge theory with a product gauge group to N = 2 gauge theory in the IR, with gauge group USp(n). The corresponding geometries are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_5} \times {S^5}}} \left/ {{\left( {{\mathbb{Z}_N} \times {\mathbb{Z}_2}} \right)}} \right.} $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_5} \times {S^5}}} \left/ {{{\mathbb{Z}_2}}} \right.} $\end{document}, respectively. We also explore more general RG flows, in which both the UV and IR CFTs are N = 2 quiver gauge theories and the corresponding geometries are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_5} \times {S^5}}} \left/ {{\left( {{\mathbb{Z}_N} \times {\mathbb{Z}_2}} \right)}} \right.} $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{Ad{S_5} \times {S^5}}} \left/ {{\left( {{\mathbb{Z}_M} \times {\mathbb{Z}_2}} \right)}} \right.} $\end{document}. Finally, we discuss the matching between the geometric and field theoretic pictures of the flows.