An algorithm based on homotopy transfer in L∞ algebras produces gauge-invariant fields for massive Kaluza-Klein modes that remain covariant under unbroken zero-mode gauge transformations.
The spectrum of the eleven-dimensional supergravity compactified on the round seven sphere,
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Homotopy transfer for massive Kaluza-Klein modes
An algorithm based on homotopy transfer in L∞ algebras produces gauge-invariant fields for massive Kaluza-Klein modes that remain covariant under unbroken zero-mode gauge transformations.