Torsion and the gravity dual of parity breaking in AdS 4/CFT 3 holography

Robert G. Leigh, Nam Nguyen Hoang, Anastasios C. Petkou

Research output: Contribution to journalArticlepeer-review


We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS 4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a ''domain wall'' between the two distinct vacua. From a bulk point of view, we point out an intriguing identification of the parameters of the torsion vortex with those of an Abrikosov vortex in a Type I superconductor. Following the analogy, we find that external Kalb-Ramond flux then appears to support bubbles of flat spacetime within an asymptotically AdS geometry.

Original languageEnglish (US)
Article number033
JournalJournal of High Energy Physics
Issue number3
StatePublished - 2009


  • AdS-CFT correspondence
  • Classical theories of gravity
  • Discrete and finite symmetries
  • Field theories in lower dimensions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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