Quantum Regge trajectories and the Virasoro analytic bootstrap

  • Scott Collier
  • Yan Gobeil
  • Henry Maxfield
  • Eric PerlmutterEmail author
Open Access
Regular Article - Theoretical Physics


Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to “double-twist” composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT2 analytic bootstrap, and extract several implications for AdS3 quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a “Virasoro Mean Field Theory” (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge c and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT2 with c > 1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin . Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in \( \sqrt{\ell } \) for fixed c. We analyze our results in various large c limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic c; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS3.


AdS-CFT Correspondence Conformal Field Theory Gauge-gravity correspondence 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Scott Collier
    • 1
  • Yan Gobeil
    • 2
  • Henry Maxfield
    • 2
    • 3
  • Eric Perlmutter
    • 4
    Email author
  1. 1.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.
  2. 2.Department of PhysicsMcGill UniversityMontrealCanada
  3. 3.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  4. 4.Walter Burke Institute for Theoretical Physics, CaltechPasadenaU.S.A.

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