TL;DR
The paper conjectures and proves that scale invariant but non-conformal field theories cannot exist in string/M-theory, extending the argument to higher dimensions and providing a classical supergravity proof.
Contribution
It offers a proof that scale invariant but non-conformal field theories are forbidden in string/M-theory, supporting the conjecture across dimensions.
Findings
Scale invariant but non-conformal theories are forbidden in (1+1) dimensions.
The proof applies in classical supergravity limit.
Implication that such theories may be forbidden in higher dimensions.
Abstract
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.
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