Generalized Gibbs ensemble and the statistics of KdV charges in 2D CFT

  • Alexander Maloney
  • Gim Seng Ng
  • Simon F. RossEmail author
  • Ioannis Tsiares
Open Access
Regular Article - Theoretical Physics


Two-dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. We study the Generalized Gibbs Ensemble with chemical potentials for these charges at high temperature. In a large central charge limit, the partition function can be computed in a saddle-point approximation. We compare the ensemble values of the KdV charges to the values in a microstate, and find that they match irrespective of the values of the chemical potentials. We study the partition function at finite central charge perturbatively in the chemical potentials, and find that this degeneracy is broken. We also study the statistics of the KdV charges at high level within a Virasoro representation, and find that they are sharply peaked.


Conformal Field Theory Integrable Hierarchies 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Alexander Maloney
    • 1
  • Gim Seng Ng
    • 2
    • 3
  • Simon F. Ross
    • 4
    Email author
  • Ioannis Tsiares
    • 1
  1. 1.Department of PhysicsMcGill UniversityMontréalCanada
  2. 2.School of MathematicsTrinity College DublinDublin 2Ireland
  3. 3.Hamilton Mathematical Institute, Trinity College DublinDublin 2Ireland
  4. 4.Centre for Particle Theory, Department of Mathematical SciencesDurham UniversityDurhamU.K.

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