AdS3 × S3 (un) twisted and squashed, and an O(2, 2; Z) multiplet of dyonic strings Original Research Article

We consider type IIB configurations carrying both NS-NS and R-R electric and magnetic 3-form charges, and whose near horizon geometry contains AdS3 × S3. Noting that S3 is a U(1) bundle over CP1 ∼ S2, we construct the dual type IIA configurations by a Hopf T-duality along the U(1) fibre. In the case where there are only R-R charges, the S3 is untwisted to S2 × S1 (in analogy with a previous treatment of AdS5 × S5). However, in the case where there are only NS-NS charges, the S3 becomes the cyclic lens space S3/Zp with its round metric (and is hence invariant when p = 1), where p is the magnetic NS-NS charge. In the generic case with NS-NS and R-R charges, the S3 not only becomes S3/Zp but is also squashed, with a squashing parameter that is related to the values of the charges. Similar results apply if we regard AdS3 as a bundle over AdS2 and T-dualise along the fibre. We show that Hopf T-dualities relate different black holes, and that they preserve the entropy. The AdS3 × S3 solutions arise as the near-horizon limits of dyonic strings. We construct an O(2, 2; Z) multiplet of such dyonic strings, where O(2, 2; Z) is a subgroup of the 0(5,5) or 0(5,21) six-dimensional duality groups, which captures the essence of the NS-NS/R-R and electric/ magnetic dualities.