QFT In the literature: partially resolved

Is the number of string vacua finite

In plain words

String theory offers many ways to curl up extra dimensions. Whether the number of distinct low-energy universes is finite is unknown.

Precise statement

Determine whether the set of string compactifications to 4D with a bounded number of light fields and effective theories valid below a fixed cutoff is finite, including whether the number of topologically distinct Calabi-Yau threefolds is finite.

What would settle it

A finiteness theorem for all compactifications below a fixed cutoff, or an infinite family of distinct consistent vacua.

Status in the literature

Finiteness of tadpole-bounded flux vacua on a fixed Calabi-Yau orientifold was proven with tame geometry (Bakker, Grimm, Schnell, Tsimerman 2021); finiteness of Calabi-Yau threefold topologies remains open.

See also