Infinite and finite consistent truncations on deformed generalised parallelisations

A bstract Given a manifold $$ \mathbbm{M} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on $$ \mathbbm{M} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> invariant under some subgroup of the group of isometries of $$ \mathbbm{M} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> . These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a ‘deformed’ generalised parallelisation starting with that on $$ \mathbbm{M} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> . This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes.