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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2005
- arXiv:
- arXiv:hep-th/0507037
- Bibcode:
- 2005hep.th....7037R
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 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