New perspectives in the duality of M-theory, heterotic strings, and F-theory

We discuss a new perspective on the dualities among sevendimensional M‑theory on elliptically fibered K3 surfaces, eight-dimensional (8D) heterotic strings on $T^2$, and 8D F‑theory on elliptic K3 surfaces. There are several distinct small-fiber F‑theory limits of a single M‑theory, and we deduce that the distinct F‑theory limits of an identical M‑theory generally include both an F‑theory limit, wherein a discrete gauge symmetry forms, and another F‑theory limit, wherein a discrete gauge symmetry does not form.

We also discuss constraints imposed on the degrees of discrete gauge groups and on the continuous gauge groups formed in F‑theory on K3 surfaces by applying a formula that is known to hold for genus-one fibrations of K3 surfaces, and by utilizing the existence of the Jacobian fibrations.

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Published 25 March 2024