Membrane Limits in Quantum Gravity

TL;DR

This paper investigates the behavior of membranes in quantum gravity limits, showing that quantum corrections prevent certain membrane limits and favor decompactification, aligning with the emergent string conjecture.

Contribution

It demonstrates that quantum corrections obstruct membrane limits at the Kaluza-Klein scale, supporting the emergent string conjecture in quantum gravity.

Findings

Quantum corrections prevent membrane limits at the Kaluza-Klein scale.

Membrane limits lead to decompactification to 11 dimensions.

Membrane behavior is consistent with the emergent string conjecture.

Abstract

It is expected that infinite distance limits in the moduli space of quantum gravity are accompanied by a tower of light states. In view of the emergent string conjecture, this tower must either induce a decompactification or correspond to the emergence of a tensionless critical string. We study the consistency conditions implied by this conjecture on the asymptotic behavior of quantum gravity under dimensional reduction. If the emergent string descends from a (2+1)-dimensional membrane in a higher-dimensional theory, we find that such a membrane must parametrically decouple from the Kaluza-Klein scale. We verify this censorship against emergent membrane limits, where the membrane would sit at the Kaluza-Klein scale, in the hypermultiplet moduli space of Calabi-Yau 3-fold compactifications of string/M-theory. At the classical level, a putative membrane limit arises, up to duality, from an M5-brane wrapping the asymptotically shrinking special Lagrangian 3-cycle corresponding to the Strominger-Yau-Zaslow fiber of the Calabi-Yau. We show how quantum corrections in the moduli space obstruct such a limit and instead lead to a decompactification to 11 dimensions, where the role of the M5- and M2-branes are interchanged.