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 [38].
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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