Lower-dimensional behavior from factorized infrared geometries along holographic RG flows

Abstract

We study the emergence of effective lower-dimensional behavior in heavy-scalar two-point functions along holographic RG flows. For charged asymptotically AdS black holes, the equal-time spatial correlator remains exponentially screened, while the temporal correlator exhibits distinct temperature-dependent regimes. Away from extremality, the controlled late-time sector is the Schwarzschild-connected saddle, whose decay rate requires matching to the full geometry. Near extremality, an AdS$_2$ throat supports an additional sector whose leading decay rate is fixed by the throat data. For RN-AdS$_4$, sufficiently near extremality, this throat contribution dominates at asymptotically late times if its matched amplitude is nonzero. At extremality, the thermal throat exponential is replaced by the AdS$_2$ power law. We also study the complete zero-density magnetic-brane flow from AdS$_5$ to AdS$_3\times \mathbb{R}^2$. The transverse heavy-scalar correlator remains exponentially screened, whereas the longitudinal correlator approaches the AdS$_3$/CFT$_2$ power law in the infrared. These results show that factorized infrared geometries can support effective lower-dimensional conformal dynamics whose realization depends on temperature, direction, and the relevant saddle sector, without implying dimensional reduction of the microscopic QFT.