Non-equilibrium dynamics of O(N) nonlinear sigma models: A large-N approach

Sumit R. Das, Krishnendu Sengupta

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17 Scopus citations


We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2 + 1 dimensions due to a time-dependent coupling in the large-N limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large N which determine the time-dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-N equations and provide explicit numerical solutions for a coupling which asymptotes to constant values in the gapped phase and approaches the zero temperature equilibrium critical point in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling g = gcdyn > gc where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of gcdyn on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in g, that the model does not display thermalization within a finite time interval t0 and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in AdS4.

Original languageEnglish
Article number72
JournalJournal of High Energy Physics
Issue number9
StatePublished - 2012


  • 1/N expansion
  • Field theories in lower dimensions
  • Nonperturbative effects
  • Sigma models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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