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

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27 Citations (Scopus)

Abstract

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
Volume2007
Issue number10
DOIs
Publication statusPublished - 2007 Oct 1

Keywords

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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    Chen, B., Cremonini, S., Lin, H., Vaman, D., Liu, J. T., Donos, A., Lin, F. L., & Wen, W. Y. (2007). Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity. Journal of High Energy Physics, 2007(10), [003]. https://doi.org/10.1088/1126-6708/2007/10/003