A note on 4D heterotic string vacua, FI-terms and the swampland

ALDAZABAL, GERARDO; L.E. IBANEZ

PHYSICS LETTERS B

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2018

0370-2693

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 compactificationwith 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 a lattice generated by massless states guarantees the instability of heterotic non-BPS extremalblackholes, as required by Weak Gravity Conjecture arguments. Thus the pervasive existence of these nearby FI-cancelling vacua would be connected with WGC arguments.