Banks-Zaks Stabilisation of Non-SUSY Strings

Abstract

It appears to be difficult within string theory to obtain genuine scale separation between spacetime and the internal sector. In this paper, we propose a novel mechanism for scale-separated vacua which hinges on stringy effects that are invisible at the level of effective field theory. We show that (meta)stable vacua can form if a super no-scale one-loop potential combines with generic two-loop contributions to the vacuum energy, in a manner analogous to Banks-Zaks fixed points. Weak string coupling and scale separation arise from the accidental smallness of the one-loop term, which receives contributions only from massive states, relative to the two-loop term. We provide a proof of concept of this mechanism in explicit non-supersymmetric heterotic toroidal orbifolds by balancing the complete one-loop contribution against the estimated two-loop term and numerically minimizing the resulting effective potential in a restricted sector of moduli space. We note that this mechanism is generically possible within any fundamental theory that has a one-loop energy that gets contributions only from massive modes.