Abstract
We compute the tree-level bosonic S matrix in light-cone gauge for superstrings on pure-NSNS AdS3 × S3 × S3 × S1. We show that it is proportional to the identity and that it takes the same form as for AdS3 × S3 × T4 and for flat space. Based on this, we make a conjecture for the exact worldsheet S matrix and derive the mirror thermodynamic Bethe ansatz (TBA) equations describing the spectrum. Despite a non-trivial vacuum energy, they can be solved in closed form and coincide with a simple set of Bethe ansatz equations — again much like AdS3 × S3 × T4 and flat space. This suggests that the model may have an integrable spin-chain interpretation. Finally, as a check of our proposal, we compute the spectrum from the worldsheet CFT in the case of highest-weight representations of the underlying Kač-Moody algebras, and show that the mirror-TBA prediction matches it on the nose.
Highlights
The supersymmetries arrange themselves into two copies of the psu(1, 1|2) superalgebra, which is enhanced to the “small” N = (4, 4) superconformal algebra in the dual CFT2 [5]
We find that the mirror thermodynamic Bethe ansatz (TBA) is not entirely trivial when no supersymmetry is manifestly preserved, but all finite-size corrections boil down to an overall shift of all energy levels, compatibly with a redefinition of the Fermi sea
We saw that the bosonic tree-level worldsheet S matrix for pure-NSNS AdS3 × S3 × S3 × S1 is proportional to the identity, and it takes the “shockwave” form [53] already found for flat-space strings [54] and for pure-NSNS AdS3 × S3 × T4 [32]
Summary
Let us write the metric of AdS3 × S3 × S3 × S1 as ds2 = RA2 dS Gμν dXμdXν = RA2 dS ds2AdS3. Following the notation of [36], we write the metric of AdS3 and S3 as ds2AdS3 = −. Where t, φ5 and φ8 are isometric coordinates. We consider a background supported by pure NSNS three-form flux: dB = RA2 dS db = 2RA2 dS. Where the determinant of the worldsheet metric γαβ has been set to −1 and the 1/RA2 dS dependence of the string tension canceled against the RA2 dS dependence of metric and. The Virasoro constraints amount to the equations of motion for the auxiliary field γαβ. For the bosonic action they are equivalent to setting C1 = 0 and C2 = 0. The Virasoro constraints impose [36].
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