The field strength, Equation (2.2), could be modified by additional coupling terms of Yang–Mills or Chapline–Manton type [20, 29] (e.g., for two 2-forms and and a 0-form , as it occurs in ten-dimensional type IIB supergravity), but we include these additional contributions to the action in “more”. Similarly, “more” might contain Chern–Simons terms, as in the action for eleven-dimensional supergravity .
We shall at this stage consider arbitrary dilaton couplings and menus of -forms. The billiard derivation given below remains valid no matter what these are; all theories described by the general action Equation (2.1) lead to the billiard picture. However, it is only for particular -form menus, spacetime dimensions and dilaton couplings that the billiard region is regular and associated with a Kac–Moody algebra. This will be discussed in Section 5. Note that the action, Equation (2.1), contains as particular cases the bosonic sectors of all known supergravity theories.
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