Exploring new constraints on Kahler moduli space of 6d N = 1 Supergravity

TL;DR

This paper establishes new consistency constraints on the Kahler moduli space of 6d N=1 supergravity theories, linking geometric conditions to the presence of certain states and symmetries, and identifying theories that belong to the Swampland.

Contribution

It introduces novel constraints derived from 5d reductions and SCFT analysis, connecting moduli space geometry with the spectrum and symmetries of 6d supergravity theories.

Findings

Constraints exclude theories with un-gauged 1-form symmetries from the landscape.

Analysis of SU(2) and U(1) models demonstrates the constraints' effectiveness.

Certain theories are shown to belong to the Swampland due to these constraints.

Abstract

We propose new constraints for 6d (1, 0) supergravity theories based on consistency conditions on the Kahler moduli spaces of their 5d reductions. The requirement that both the metric and the BPS string tensions in the Kahler moduli space are positive imposes specific restrictions on the Chern-Simons coefficients in the 5d effective Lagrangians that are derived from the Kaluza-Klein reductions of 6d theories. Moreover, the emergence of local interacting 5d CFTs when the moduli space metric degenerates introduces additional constraints coming from the analysis of 5d SCFTs. Focusing on the moduli spaces of 6d supergravity theories without a tensor multiplet and their Higgsings, we show that these constraints require the presence of certain primary states in the 2d worldvolume CFTs on 1/2 BPS strings. We specifically analyze a class of SU(2) models and infinite families of U(1) models using these constraints, and demonstrate that the theories featuring a 1-form symmetry in their massless spectra, unless the 1-form symmetry is gauged, fail to satisfy the constraints and therefore belong to the Swampland.