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String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x U(1)_L.
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W. Song and A. Strominger, “Warped AdS3/Dipole-CFT Duality,” JHEP 1205
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