  Scale invariant but non-conformal field theories are forbidden in (1+1)
dimension, and so should be the corresponding holographic dual gravity
theories. We conjecture that such scale invariant but non-conformal field
configurations do not exist in the string/M-theory. We provide a proof of this
conjecture in the classical supergravity limit under a certain gauge condition.
Our proof does also apply in higher dimensional scale invariant but
non-conformal field configurations, which suggests that scale invariant but
non-conformal field theories may be forbidden in higher dimensions as well.
