Minimal AdS₃

We show that type IIB string theory on AdS₃ × S ³ × M₄ with p units of NS flux contains an integrable subsector, isomorphic to the minimal (p, 1) bosonic string. To this end, we construct a topological string theory with target space Euclidean AdS₃ × S³. We use a variant of Hamiltonian reduction to prove its equivalence to the minimal (p, 1) string. The topological theory is then embedded in the physical 10-dimensional IIB string theory. Correlators of tachyons in the minimal string are mapped to correlators of spacetime chiral primaries in the IIB theory, in the presence of background 5-form RR flux. We also uncover a ground ring structure in AdS₃ × S³ analogous to the well-known ground ring of the minimal string. This tractable model provides a literal incarnation of the idea that the holographic direction of AdS space is the Liouville field. We discuss a few generalizations; in particular, we show that the N = 4 topological string on an A_p-1 ALE singularity also reduces to the (p, 1) minimal string.