AdS3xS3 (un)twisted and squashed, and an O(2, 2;Z) multiplet of dyonic strings

We consider type IIB configurations carrying both NS-NS and R-R electric and magnetic 3-form charges, and whose near horizon geometry contains AdS(3) x S-3. Noting that S' is a U(1) bundle over CP1 similar to S-2, 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 S-3 is untwisted to S-2 x S-1 (in analogy with a previous treatment of AdS(5) x S-5). However, in the case where there are only NS-NS charges, the S-3 becomes the cyclic lens space S-3/Z(p) 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 S-3 not only becomes S-3/Z(p) but is also squashed, with a squashing parameter that is related to the values of the charges. Similar results apply if we regard AdS(3) as a bundle over AdS(2) and T-dualise along the fibre. We show that Hopf T-dualities relate different black holes, and that they preserve the entropy. The AdS(3) x S-3 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 O(5,5) or O(5,21) six-dimensional duality groups, which captures the essence of the NS-NS/R-R and electric/magnetic dualities. (C) 1999 Elsevier Science B.V.