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Title: Is the number of string vacua finite
Plain: String theory offers many ways to curl up extra dimensions. Whether the number of distinct low-energy universes is finite is unknown.
Precise: 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.
Settled by: A finiteness theorem for all compactifications below a fixed cutoff, or an infinite family of distinct consistent vacua.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: (empty)