No Forbidden Landscape in String/M-theory

TL;DR

The paper argues that scale-invariant but non-conformal field theories in $(1+1)$ dimensions have no consistent holographic dual within string/M-theory. It formulates and tests a gravitational counterpart to Polchinski's theorem, proving in the classical supergravity limit that scale invariance enhances to conformal invariance under a specific gauge and the null energy condition, with extensions to higher dimensions. It further analyzes how higher-derivative corrections must align with this constraint, using DBI-like examples to illustrate possible consistency requirements and highlighting potential swampland implications. Overall, the work suggests a broad prohibition on scale-invariant but non-conformal configurations in string/M-theory and frames stringent conditions on UV completions that include higher-derivative terms.

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.