String theory on AdS3 and the symmetric orbifold of Liouville theory

Abstract

For string theory on AdS 3 with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows us to show that the CFT dual of superstring theory on AdS 3 × S 3 × T 4 for generic NS-NS flux is the symmetric orbifold of (N = 4 Liouville theory) × T 4 . For the case of minimal flux (k = 1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T 4 , thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS 3 × X.

Correlators of the symmetric product orbifold

“…In [20], a natural extension of this idea was proposed. It was noticed that for higher values of NS-NS flux, the perturbative long-string spectrum matches that of a symmetric product orbifold of N = 4 Liouville theory tensored with T 4 .…”

AdS3 solutions with from S3 × S3 fibrations

“…for Ψ ± both real. Supersymmetry is then ensured in IIA when the following conditions hold 7 . Specifically these are the conditions when one assumes that…”

“…These are charged SO(3) D forms 7 , they depend on the index 1 because we took 1,2 = 1 1,2 as our explicit  = 1 sub-sector, taking 1,2 = i 1,2 leads to a dependence on i, but any choice of  = 1 7 Technically they contain both a charged and singlet contribution: One can construct matrix bi spinors Φ ij = i 1 ⊗ j † 2 which are a tensor product of SO(3) triplets and so decompose into respectively singlet, anti-symmetric and symmetric traceless irreducible representations as 3 ⊗ 3 = 1 ⊕ 3 ⊕ 5. As it is sufficient, here we are only considering the component Φ 11 , so only the 1 and (11) component of the 5 appearthe forms of (3.7) are a linear combination of both.…”

“…In part this is due to the relative tractability of CFTs in two dimensions, moreover there has also been significantly more progress made towards quantising string theory in AdS 3 backgrounds (see the seminal works [1][2][3] ) than in higher dimensional AdS cases. This provides powerful tools to probe the AdS-CFT correspondence, even beyond the strict large N limit of CFTs and classical limit of supergravity (see the recent works [4][5][6][7] and references therein).…”

String theory on AdS3 × M7 in the tensionless limit

“…Very recently, the interest in superstrings on AdS 3 × S 3 × M 4 has been renewed [7], and very interesting new results have been obtained [8,9,10,11,12,13,14,15,16,17], especially in the context of AdS 3 /CFT 2 . Much of the attention in the recent studies is focused on the special limit in which the string length √ α equals R, the radius of AdS 3 space.…”