Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds

TL;DR

This work constructs a complete non-linear Kaluza-Klein reduction of IIB supergravity on Sasaki–Einstein 5-manifolds to five dimensions, retaining the bosonic fields in the breathing/squashing multiplets up to KK level $n=2$ and yielding a $D=5$, $N=2$ gauged supergravity coupled to massive multiplets. The reduction uses the SE$_5$ structure to decompose the ten-dimensional fields into five-dimensional degrees of freedom, and the authors derive an explicit 5D Lagrangian that reproduces the reduced equations of motion, including a Chern–Simons term and a shift of the graviphoton. Linearized KK analysis identifies the full low-lying spectrum with masses $m^2=-3,8,9,12,16,21,24,32$ organized into $ ext{SU}(2,2|1)$ multiplets across KK levels $n=0,1,2$, and the results yield several consistent truncations that connect to holographic superconductor models and non-relativistic holography. The work confirms a conjecture that consistent massive truncations can be obtained by restricting to singlets on the Kahler–Einstein base and truncating to the lowest modes in the massive trajectories, providing UV-complete frameworks for AdS/CMT applications and offering groundwork for future fermionic extensions and AdS/CMT phenomenology.

Abstract

Recent work on holographic superconductivity and gravitational duals of systems with non-relativistic conformal symmetry have made use of consistent truncations of D=10 and D=11 supergravity retaining some massive modes in the Kaluza-Klein tower. In this paper we focus on reductions of IIB supergravity to five dimensions on a Sasaki-Einstein manifold, and extend these previous truncations to encompass the entire bosonic sector of gauged D=5, N=2 supergravity coupled to massive multiplets up to the second Kaluza-Klein level. We conjecture that a necessary condition for the consistency of massive truncations is to only retain the lowest modes in the massive trajectories of the Kaluza-Klein mode decomposition of the original fields. This is an extension of the well-known result that consistent truncations may be obtained by restricting to the singlet sector of the internal symmetry group.