  Motivated by its potential use in constraining the structure of 6D
renormalization group flows, we determine the low energy dilaton-axion
effective field theory of conformal and global symmetry breaking in 6D
conformal field theories (CFTs). While our analysis is largely independent of
supersymmetry, we also investigate the case of 6D superconformal field theories
(SCFTs), where we use the effective action to present a streamlined proof of
the 6D a-theorem for tensor branch flows, as well as to constrain properties of
Higgs branch and mixed branch flows. An analysis of Higgs branch flows in some
examples leads us to conjecture that in 6D SCFTs, an interacting dilaton
effective theory may be possible even when certain 4-dilaton 4-derivative
interaction terms vanish, because of large momentum modifications to 4-point
dilaton scattering amplitudes. This possibility is due to the fact that in all
known $D > 4$ CFTs, the approach to a conformal fixed point involves effective
strings which are becoming tensionless.
