Consistent truncation and generalized duality based on exceptional generalized cosets
Falk Hassler, Yuho Sakatani
TL;DR
The paper develops a comprehensive, algebraic framework for consistent truncations in supergravity using exceptional generalized cosets, enabling truncations with arbitrary supersymmetry and unveiling generalized dualities as intrinsic to the double coset structure $M=G_S\backslash G / H$. By constructing generalized frames and covariant curvatures entirely from algebraic data (structure constants and invariant tensors), the approach yields constant intrinsic torsion $\mathcal{T}_{AB}{}^C$ and covariant generalized Riemann tensors, obviating the need to solve differential equations. The formalism unifies generalized Scherk--Schwarz reductions with nontrivial structure groups, clarifying how different higher-dimensional backgrounds can truncate to the same lower-dimensional theory via generalized dualities, and extends naturally from DFT to exceptional field theory. The framework is illustrated with explicit examples in DFT and ExFT, including standard and generalized cosets, and culminates in detailed constructions of truncations and dualities such as non-abelian T-duality within concrete backgrounds. These results provide a versatile, purely algebraic pathway to generate and relate consistent truncations and their uplifts across diverse duality frames, with broad implications for constructing gauged supergravities and exploring U-/T-duality webs.
Abstract
We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\GS \backslash G/H$. This approach generalizes the well-established generalized Scherk-Schwarz reductions on generalized parallelizable spaces $G/H$, which preserve maximal supersymmetry, to scenarios with reduced supersymmetry by introducing a non-trivial generalized structure group $\GS$. The double coset structure plays two distinct roles: for a given $G$, the choice of subgroup $\GS$ determines the (constant) generalized torsion/curvature and the pattern of supersymmetry breaking, while $H$ parameterizes inequivalent supergravity backgrounds that share the same truncated theory. The entire construction proceeds algebraically, systematically building $\GS$-invariant tensors from generalized frame fields, with the intrinsic torsion automatically constant and a $\GS$-singlet. Different choices of $H$ lead to distinct higher-dimensional backgrounds that truncate to the same lower-dimensional theory, thereby realizing U-duality. We illustrate the framework through explicit examples in double field theory and exceptional field theory.