  Theories with generalised conformal structure contain a dimensionful
parameter, which appears as an overall multiplicative factor in the action.
Examples of such theories are gauge theories coupled to massless scalars and
fermions with Yukawa interactions and quartic couplings for the scalars in
spacetime dimensions other than 4. Many properties of such theories are similar
to that of conformal field theories (CFT), and in particular their 2-point
functions take the same form as in CFT but with the normalisation constant now
replaced by a function of the effective dimensionless coupling $g$ constructed
from the dimensionful parameter and the distance separating the two operators.
Such theories appear in holographic dualities involving non-conformal branes
and this behaviour of the correlators has already been observed at strong
coupling. Here we present a perturbative computation of the two-point function
of the energy-momentum tensor to two loops in dimensions $d= 3, 5$, confirming
the expected structure and determining the corresponding functions of $g$ to
this order, including the effects of renormalisation. We also discuss the d=4
case for comparison. The results for $d=3$ are relevant for holographic
cosmology, and in this case we also study the effect of a $\Phi^6$ coupling,
which while marginal in the usual sense it is irrelevant from the perspective
of the generalised conformal structure. Indeed, the effect of such coupling in
the 2-point function is washed out in the IR but it modifies the UV.
