Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model

A. Dei (Institut für theoretische Physik, ETH Zürich, Wolfgang-Pauli-Strasse 27, Zürich, 8093, Switzerland) ; A. Sfondrini (Institut für theoretische Physik, ETH Zürich, Wolfgang-Pauli-Strasse 27, Zürich, 8093, Switzerland)

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.

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      "source": "Springer", 
      "value": "We compute the tree-level bosonic S matrix in light-cone gauge for superstrings on pure-NSNS AdS3 \u00d7 S3 \u00d7 S3 \u00d7 S1. We show that it is proportional to the identity and that it takes the same form as for AdS3 \u00d7 S3 \u00d7 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 \u2014 again much like AdS3 \u00d7 S3 \u00d7 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 Ka\u010d-Moody algebras, and show that the mirror-TBA prediction matches it on the nose."
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Published on:
07 May 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 2
Pages 1-39
DOI:
https://doi.org/10.1007/JHEP02(2019)072
arXiv:
1812.08195
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

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