A Supersymmetric and Smooth Compactification of M-theory to AdS(5)

TL;DR

The paper constructs a supersymmetric, smooth $AdS_5$ background in M-theory with an internal $S^4$ bundle over $S^2$, governed by two diagonal monopole charges, yielding an ${\cal N}=2$ AdS$_5$ solution dual to an ${\cal N}=1$ D=4 SCFT. It extends this construction to analogous warped AdS embeddings of $AdS_4$, $AdS_3$, and $AdS_2$ in massive IIA, Type IIB, and M-theory, with internal spaces realized as $S^n$ bundles over $S^2$ or $H^2$ and exhibiting generalized holonomy, including a nine-dimensional example. The authors provide explicit warp-factor Ansätze, first-order BPS equations, and uplift formulas, yielding both smooth and singular backgrounds and clarifying when bundles are trivial or twisted. Together, these results expand the landscape of supersymmetric warped compactifications and provide concrete settings to explore AdS/CFT and generalized holonomy.

Abstract

We obtain smooth M-theory solutions whose geometry is a warped product of AdS_5 and a compact internal space that can be viewed as an S^4 bundle over S^2. The bundle can be trivial or twisted, depending on the even or odd values of the two diagonal monopole charges. The solution preserves N=2 supersymmetry and is dual to an N=1 D=4 superconformal field theory, providing a concrete framework to study the AdS_5/CFT_4 correspondence in M-theory. We construct analogous embeddings of AdS_4, AdS_3 and AdS_2 in massive type IIA, type IIB and M-theory, respectively. The internal spaces have generalized holonomy and can be viewed as S^n bundles over S^2 for n=4, 5 and 7. Surprisingly, the dimensions of spaces with generalized holonomy includes D=9. We also obtain a large class of solutions of AdS\times H^2.