Minimal AdS_3

TL;DR

This paper demonstrates that Type IIB string theory on AdS_3 X S^3 with NS flux contains an integrable subsector equivalent to the minimal (p,1) bosonic string, revealing a deep connection between AdS holography and minimal string models.

Contribution

The authors construct a topological string theory on AdS_3 X S^3 and prove its equivalence to the minimal (p,1) string, establishing a new integrable subsector within Type IIB string theory.

Findings

Identified an integrable subsector in AdS_3 X S^3 with NS flux

Mapped correlators of minimal string tachyons to IIB spacetime correlators

Discovered a ground ring structure analogous to the minimal string

Abstract

We show that Type IIB string theory on AdS_3 X S^3 X M_4 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 AdS_3 X S^3. 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 ten-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 AdS_3 X S^3 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.