Type 0A string theory is the non-supersymmetric cousin of Type IIA. It has a tachyon — an instability in its spectrum — that condenses at strong coupling, but its geometric origin in M-theory has been unclear. The standard M-theory description of Type IIA uses compactification on a circle. What geometry gives Type 0A?
Baykara, Dudas, and Vafa propose: M-theory on a wedge of two circles (S¹ ∨ S¹), both sub-Planckian. The wedge sum — two circles touching at a point — is topologically distinct from a single circle or a torus. The sub-Planckian sizes mean that quantum effects dominate the geometry, causing fields to inhabit different resolutions of the space.
Tachyon condensation maps to geometry: one circle shrinks, and the wedge reduces to a single circle — recovering the supersymmetric Type IIA theory. The tachyon's instability is the geometric instability of the wedge under one circle's collapse. Supersymmetry isn't broken by a field-theoretic mechanism; it's absent because the geometry is wrong, and it's restored when the geometry simplifies.
Using F-theory methods, the authors describe the Type 0B dual and find a strong-coupling critical point with Γ₀(2) ⊂ SL(2,Z) duality symmetry. This critical point is an unstable de Sitter vacuum — a cosmologically relevant feature of a non-supersymmetric string theory.
A sub-Planckian figure-eight. Two circles touching at a point. The geometry that breaks supersymmetry.