Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture

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 α′ 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 α′-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.

The EFT stringy viewpoint on large distances

“…One may be skeptic about the reliability of these conclusions, since the volume of the fibral curve C 2 shrinks to zero size. However, this EFT flow is a particular realisation of a J-class A limit of [20,100], in which it is argued that there exists a dual weakly coupled heterotic description in which the D3-brane wrapping C 2 is dualised to a F1-string. The…”

“…In fact, the above results should qualitatively hold for more general J-class A limits with heterotic dual, in which X is a more general P 1 -fibration. The D3-brane wrapping the P 1 -fibre is an example of elementary EFT string that, borrowing the results of [20,100], satisfies 2 with scaling weight w = 1 and is non-degenerate.…”

“…As a consequence of this conjecture, quantum gravity would impose a maximal size to any EFT field space. Determining what this size is and what is the precise mechanism that triggers the EFT breakdown is a central part of the Swampland Program [2][3][4][5], and substantial progress has been achieved through different studies and refinements of the SDC [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

F-theory flux vacua at large complex structure

“…Moduli stabilisation in type IIB string theory around such regions has been considered in [62,63]. Furthermore, for three-folds such limits have been classified in the dual Kähler moduli space as emergent string/decompactification limits in [50], see also [64,65] for a discussion of similar emergent string limits in CY four-folds. Since such limits are defined in the large volume phase of the mirror dual four-fold, it should be easier to relate them to the discussion presented in here.…”

Tackling the SDC in AdS with CFTs

“…The SDC has been mainly studied in the context of four- [11][12][13][14][15][16][17][18] or six-dimensional [19] Minkowski theories with eight or more supercharges obtained by dimensional reduction of type II string theories, or their lifts to strong coupling. Using the beautifully-intricate web JHEP08(2021)057 of dualities of string theory, it was proposed that the tower of massless states corresponds to either a decompactification limit or a tensionless weakly-coupled fundamental string in disguise [14][15][16], although it may be required to take quantum corrections into account to make them manifest [16,[20][21][22]. Note that, in the latter case, the tower of states generically contains arbitrarily large higher-spin fields.…”