Minimal AdS_3
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 tendimensional 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 5form RR flux. We also uncover a ground ring structure in AdS_3 X S^3 analogous to the wellknown 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_{p1} ALE singularity also reduces to the (p,1) minimal string.
 Publication:

arXiv eprints
 Pub Date:
 July 2005
 arXiv:
 arXiv:hepth/0507037
 Bibcode:
 2005hep.th....7037R
 Keywords:

 High Energy Physics  Theory
 EPrint:
 v2: 60 pages, 2 figures. New section on relation to topological strings on ALE. Added a clarification on the relation with N=2 minimal models coupled to topological gravity. Added references