Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

Abstract

We propose quantum gravitational constraints on effective four-dimensional theories with $$ \mathcal{N} $$ N = 1 supersymmetry. These Swampland constraints arise by demanding consistency of the worldsheet theory of a class of axionic, or EFT, strings whose existence follows from the Completeness Conjecture of quantum gravity. Modulo certain assumptions, we derive positivity bounds and quantization conditions for the axionic couplings to the gauge and gravitational sector at the two- and four-derivative level, respectively. We furthermore obtain general bounds on the rank of the gauge sector in terms of the gravitational couplings to the axions. We exemplify how these bounds rule out otherwise consistent effective supergravity theories as theories of quantum gravity. Our derivations of the quantum gravity bounds are tested and further motivated in concrete string theoretic settings. In particular, this leads to a sharper version of the bound on the gauge group rank in F-theory on elliptic four-folds with a smooth base, which improves the known geometrical Kodaira bounds. We furthermore provide a detailed derivation of the EFT string constraints in heterotic string compactifications including higher derivative corrections to the effective action and apply the bounds to M-theory compactifications on G2 manifolds.

Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

“…However, in the more general Type IIB EFTs axions participate in the generalized θ-terms, and the associated continuous shift symmetries are broken down to discrete ones. Consequently, as also highlighted in the recent [46], the standard dualization procedure summarized in appendix A cannot be generally performed, and the Noether procedure cannot be straightforwardly applied in order to compute the eventual one-form currents. Nevertheless, it is worth remarking that the one-form currents J i B = da i still appear to be conserved, and well-defined -see [47,48].…”

Supergravity EFTs and swampland constraints

“…When introduced in the effective description as probes, one can derive consistency conditions for the whole theory by demanding consistency of the probe. This approach has been followed in five dimensions in [102] and more recently in four dimensional N = 1 supergravity in [99]. Before entering the discussion of [99], we would like to review how strings and membranes can be introduced into the setup of minimal supergravity in four dimensions.…”

“…This approach has been followed in five dimensions in [102] and more recently in four dimensional N = 1 supergravity in [99]. Before entering the discussion of [99], we would like to review how strings and membranes can be introduced into the setup of minimal supergravity in four dimensions.…”

“…Such a step can be motivated by the completeness hypothesis [96]. This approach has been recently pursued in [97][98][99][100][101] (see [102] for a similar work in five dimensions), based on the manifest supersymmetric formalism developed in [103,104], but the history of supergravity coupled to extended objects dates back to [105,106].…”

“…In this section, we briefly review these recent developments, with particular focus on [99], since they provide a somehow complementary approach to the one we presented above. Any misconception in the presentation of the work by other authors is of course ours.…”