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Keywords
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classical integrability, conformal symmetry, Poisson–Lie T-duality, string duality, 𝜎-model
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Abstract
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The author proceed to construct a dual pair for the AdS3 × S3 background by
applying non-Abelian T-duality (here as Poisson–Lie [PL] T-duality on a
semi-Abelian double). By using a certain parametrization of the 4-dimensional
Lie group A2 ⊗ 2A1 and by a suitable choice of spectator-dependent matrices
the original 𝝈-model including the AdS3 × S3 metric and a non-trivial B-field
are constructed. The dual background constructed by means of the PL
T-duality with the spectators is an asymptotically flat one with a potential
black hole interpretation supported by a non-trivial H-flux whose metric
contains the true singularity with a single horizon. The question of classical
integrability of the non-Abelian T-dual 𝝈-models under consideration is
addressed, and their corresponding Lax pairs are found, depending on some
spectral parameters. Finally, the conformal invariance conditions of the
models are checked up to two-loop order, and it has been concluded that the
resulting model is indeed a solution of supergravity.
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