Tri-vector deformations with external fluxes

We extend the formalism of tri-vector deformations to the full SL(5) exceptional field theory with no truncation assumed thus covering 11D backgrounds of any form. We derive explicit transformation rules for 11D supergravity component fields and prove that these generate solutions given the same algebraic conditions hold: generalized Yang-Baxter equation and the unimodularity condition.

💡 Research Summary

The paper presents a comprehensive extension of tri‑vector (or “tri‑form”) deformations to the full SL(5) exceptional field theory (ExFT) without any truncation, thereby covering arbitrary eleven‑dimensional supergravity backgrounds. The authors begin by performing a full 7 + 4 Kaluza‑Klein split of the 11‑dimensional metric, three‑form and associated gauge fields, keeping dependence on all eleven coordinates. They rewrite the eleven‑dimensional vielbein in an upper‑triangular form, introduce the internal scalar matrix (\phi_{m}{}^{\bar m}), the Kaluza‑Klein vectors (A_{\mu}{}^{m}), and decompose the three‑form into a hierarchy of mixed components (A_{\mu\nu m}, A_{\mu mn}, A_{mnk}) etc. All these objects are then embedded into the SL(5) ExFT language: the generalized vielbein (\mathcal{E}{M}{}^{\bar M}) (a 5 × 5 matrix of unit determinant) encodes the scalars, the ten SL(5) vectors (A{\mu}^{