RG flows from Spin(7), CY 4-fold and HK manifolds to AdS, Penrose limits and pp waves

TL;DR

The paper constructs explicit holographic RG flows from M-theory backgrounds with Spin(7) holonomy, CY4 folds, and HK geometry to IR AdS$_4$ backgrounds, realized as D2–D6 brane systems with D6 wrapping supersymmetric four-cycles and dynamical $F_4$ flux. By working in eight-dimensional $SU(2)$ gauged supergravity and uplifting to eleven dimensions, it produces flows to $AdS_4\times\tilde{S^7}$, $AdS_4\times Q^{1,1,1}$, and $AdS_4\times N^{0,1,0}$, corresponding to dual 3D SCFTs with ${\cal N}=1,2,3$ supersymmetry, respectively, and analyzes the operator spectra near fixed points. Penrose limits are computed to yield pp-wave backgrounds, revealing supersymmetry enhancement to ${\cal N}=8$ in the BMN-like sectors of the dual theories. The work also explores RG flows from 6D gauged supergravity with uplifts to massive IIA, presenting both supersymmetric and non-supersymmetric interpolations and outlining future directions for flux-resolved singularity resolution and higher-dimensional extensions.

Abstract

We obtain explicit realizations of holographic renormalization group (RG) flows from M-theory, from E^{2,1} \times Spin(7) at UV to AdS_4 \times \tilde{S^7} (squashed S^7) at IR, from E^{2,1} \times CY4 at UV to AdS_4 \times Q^{1,1,1} at IR, and from E^{2,1} \times HK (hyperKahler) at UV to AdS_4 \times N^{0,1,0} at IR. The dual type IIA string theory configurations correspond to D2-D6 brane systems where D6 branes wrap supersymmetric four-cycles. We also study the Penrose limits and obtain the pp-wave backgrounds for the above configurations. Besides, we study some examples of non-supersymmetric and supersymmetric flows in five-dimensional gauge theories.