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We extend the construction of bubbling 1/2 BPS solutions of Lin, Lunin and Maldacena (H. Lin, O. Lunin, J. Maldacena, JHEP 0410 (2004) 025, hep-th/0409174 ) in two directions. First we enquire whether bubbling 1/2 BPS solutions can be constructed in minimal 6d supergravity and second we construct solutions that are 1/4 BPS in type IIB. We find that the S 1 × S 1 bosonic reduction of ( 1 , 0 ) 6d supergravity to 4d gravity coupled to 2 scalars and a gauge field is consistent only provided that the gauge field obeys a constraint ( F ∧ F = 0 ). This is to be contrasted to the case of the S 3 × S 3 bosonic reduction of type IIB supergravity to 4d gravity, 2 scalars and a gauge field, where consistency is achieved without imposing any such constraints. Therefore, in the case of ( 1 , 0 ) 6d supergravity we are able to construct 1/2 BPS solutions, similar to those derived in type IIB, provided that this additional constraint is satisfied. This ultimately prohibits the construction of a family of 1/2 BPS solutions corresponding to a bubbling AdS 3 × S 3 geometry. Returning to type IIB solutions, by turning on an axion–dilaton field we construct a family of bubbling 1/4 BPS solutions. This corresponds to the inclusion of back-reacted D7 branes to the solutions of Lin, Lunin and Maldacena. |
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