Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture

TL;DR

This paper investigates quantum corrections in 4d N=1 supersymmetric theories, confirming the Emergent String Conjecture and analyzing their impact on the Weak Gravity Conjecture, revealing how quantum effects modify classical bounds and the structure of infinite distance limits.

Contribution

It provides a detailed analysis of quantum corrections in N=1 F-theory compactifications, confirming the Emergent String Conjecture and proposing modifications to the Weak Gravity Conjecture at the quantum level.

Findings

Quantum corrections obstruct certain infinite distance limits with low-tension strings.

Limits with string tension at the Kaluza-Klein scale are not obstructed.

Gauge threshold corrections modify the super-extremality bound in 4d theories.

Abstract

We study quantum corrections in four-dimensional theories with $N=1$ supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of $N=1$ supersymmetric F-theory compactifications to four dimensions including perturbative $\alpha'$ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed. In the second part of the paper we study the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory $\alpha'$ corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.