Gravitational and Yang-Mills instantons in holographic RG flows

We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ 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 $Ad{S}_3\times S^3\mathrm{/}{\mathbb{Z}}_N$ and $Ad{S}_3\times S^3$ 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${}^{\mathrm{\prime }}$ context. In type IIB theory, the flow interpolates between $Ad{S}_5\times S^5\mathrm{/}{\mathbb{Z}}_N$ and $AdS_5\times S^5$geometries\mathrm{.}ThefieldtheoryinterpretationisthatofanN=2$SU(n)^N$quivergaugetheoryflowingtoN=4SU(n)gaugetheory\mathrm{.}IntypeI$’$ 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 $AdS_5\times S^5/($\mathbb{Z}$_N\times $\mathbb{Z}$_2)$and$AdS_5\times S^5/$\mathbb{Z}$_2$, 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 $AdS_5\times S^5/($\mathbb{Z}$_N\times $\mathbb{Z}$_2)$and$AdS_5\times S^5/($\mathbb{Z}$_M\times $\mathbb{Z}$_2)$. Finally, we discuss the matching between the geometric and field theoretic pictures of the flows.