Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Bin Chen, Sera Cremonini, Hai Lin, Diana Vaman, James T. Liu, Aristomenis Donos, Feng Li Lin, Wen Yu Wen

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


This paper focuses on supergravity duals of BPS states in = 4 super Yang-Mills. In order to describe these duals, we begin with a sequence of breathing mode reductions of IIB supergravity: first on S 3, then S 3 × S 1, and finally on S 3 × S 1 × CP 1. We then follow with a complete supersymmetry analysis, yielding 1/8, 1/4 and 1/2 BPS configurations, respectively (where in the last step we take the Hopf fibration of S 3). The 1/8 BPS geometries, which have an S 3 isometry and are time-fibered over a six-dimensional base, are determined by solving a non-linear equation for the Kähler metric on the base. Similarly, the 1/4 BPS configurations have an S 3 × S 1 isometry and a four-dimensional base, whose Kähler metric obeys another non-linear, Monge-Ampère type equation. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S 3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS 5 × S 5 ground state corresponds to excising the interior of an S 5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S 5 and/or the excision of additional droplets from the base. In the case of 1/4 BPS configurations, by enforcing regularity conditions, we identify three-dimensional surfaces inside the four-dimensional base which separate the regions where the S 3 shrinks to zero size from those where the S 1 shrinks. We discuss a large class of examples to show the emergence of a universal bubbling AdS picture for all 1/2, 1/4 and 1/8 BPS geometries.

Original languageEnglish
Article number003
JournalJournal of High Energy Physics
Issue number10
Publication statusPublished - 2007 Oct 1


  • AdS-CFT correspondence
  • Gauge-gravity correspondence
  • M-theory
  • Superstring vacua

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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