Shear modes, criticality and extremal black holes

Mohammad Edalati, Juan I. Jottar, Robert G. Leigh

Research output: Contribution to journalArticlepeer-review


We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordström AdS4 black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordström AdS4 black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential μ fixed.

Original languageEnglish (US)
Article number75
JournalJournal of High Energy Physics
Issue number4
StatePublished - 2010


  • AdS-CFT correspondence
  • Black holes in string theory
  • Gauge-gravity correspondence

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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