Abstract
We propose Swampland constraints on consistent 5-dimensional mathcal{N} = 1 supergravity theories. We focus on a special class of BPS magnetic monopole strings which arise in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT. In M-theory, where these theories are realized by compactification on Calabi-Yau 3-folds, the special monopole strings arise from wrapped M5-branes on special (“semi-ample”) 4-cycles in the threefold. We identify various necessary geometric conditions for such cycles to lead to requisite BPS strings and translate these into constraints on the low-energy theories of gravity. These and other geometric conditions, some of which can be related to unitarity constraints on the monopole worldsheet, are additional candidates for Swampland constraints on 5-dimensional mathcal{N} = 1 supergravity theories.
Highlights
(up to deformations) to a finite set
The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT
In [3] it was shown that the assumption of existence of BPS strings in these theories, and the requirement of having a unitary theory on their worldsheet, leads to severe restrictions and it was shown that this rules out some infinite class of anomaly free matter spectrum that is not possible to construct from string theory
Summary
On the Coulomb branch of the moduli space, the low-energy spectrum includes 1/2 BPS extended objects magnetically charged under the Abelian gauge groups. The low-energy theory on the special vacua is described by the gauge theory of the enhanced gauge group G coupled to the massless charged hypermultiplets. The gauge coupling hi is given by a linear sum of the scalar values φα in the Abelian part, such as r+1−r hi = These scalar moduli φα parametrize the special sub-manifold of the moduli space where the gauge symmetry enhancement occurs. At a generic point on the Coulomb branch, the effective theory after integrating out all the massive charged fields always reduces to an Abelian gauge theory description. Such theories will be discussed in more details
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