  Sum rules in effective field theories, predicated upon causality, place
restrictions on scattering amplitudes mediated by effective contact
interactions. Through unitarity of the $S$-matrix, these imply that the size of
higher dimensional corrections to transition amplitudes between different
states is bounded by the strength of their contributions to elastic forward
scattering processes. This places fundamental limits on the extent to which
hypothetical symmetries can be broken by effective interactions. All analysis
is for dimension $8$ operators in the forward limit. Included is a thorough
derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$
global symmetry representations resembling those of the Standard Model, general
bounds on flavour violation, new bounds for interactions between particles of
different spin, inclusion of loops of dimension $6$ operators and illustration
of the resulting strengthening of positivity bounds over tree-level
expectations, a catalogue of supersymmetric effective interactions up to mass
dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the
positivity theorems as well as the new bounds.
