A Note on 4D Heterotic String Vacua, FI-terms and the Swampland

Abstract

We present a conjecture for the massless sector of perturbative 4D $N=1$ heterotic $(0,2)$ string vacua, including $U(1{)}^n$ gauge symmetries,one of them possibly anomalous (like in standard heterotic compactifications). Mathematically it states that the positive hull generated by the charges of the massless chiral multiplets spans a sublattice of the full charge lattice. We have tested this conjecture in many heterotic $N=1$ compactifications in 4D. Our motivation for this conjecture is that it allows to understand a very old puzzle in $(0,2)$ $N=1$ heterotic compactification with an anomalous $U(1)$. The conjecture guarantees that there is always a D-flat direction cancelling the FI-term and restoring $N=1$ SUSY in a nearby vacuum. This is something that has being verified in the past in a large number of cases, but whose origin has remained obscure for decades. We argue that the existence of this lattice of massless states guarantees the instability of heterotic non-BPS extremal blackholes, as required by Weak Gravity Conjecture arguments. Thus the pervasive existence of these nearby FI-cancelling vacua would be connected with WGC arguments.

11 pages, no figures

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• Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Modular Symmetries and the Swampland Conjectures
• A Strong Scalar Weak Gravity Conjecture and Some Implications
• Supersymmetric Protection and the Swampland
• The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture
• Three-forms and Fayet-Iliopoulos terms in Supergravity: Scanning Planck mass and BPS domain walls