skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum Regge trajectories and the Virasoro analytic bootstrap

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4]
  1. Harvard Univ., Cambridge, MA (United States)
  2. McGill Univ., Montreal, QC (Canada)
  3. McGill Univ., Montreal, QC (Canada); Univ. of California, Santa Barbara, CA (United States)
  4. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
+ Show Author Affiliations

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 ℓ. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in √ℓ 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.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; Walter Burke Institute for Theoretical Physics; Natural Sciences and Engineering Research Council of Canada (NSERC); National Science Foundation (NSF)
Grant/Contract Number:
SC0011632; 488657; PHY-1748958
OSTI ID:
1611635
Journal Information:
Journal of High Energy Physics (Online), Vol. 2019, Issue 5; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 51 works
Citation information provided by
Web of Science

References (110)

Virasoro conformal blocks and thermality from classical background fields journal November 2015
Solving the Schwarzian via the conformal bootstrap journal August 2017
Bootstrapping the spectral function: on the uniqueness of Liouville and the universality of BTZ journal September 2018
Eternal black holes in anti-de Sitter journal April 2003
Charged structure constants from modularity text January 2017
The analytic bootstrap and AdS superhorizon locality journal December 2013
Anomalous dimensions at finite conformal spin from OPE inversion journal November 2018
An exact operator that knows its location journal February 2018
Higgsing the stringy higher spin symmetry text January 2015
New properties of large-c conformal blocks from recursion relation journal July 2018
Higgsing the stringy higher spin symmetry journal October 2015
Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications journal July 2018
Analyticity in spin in conformal theories journal September 2017
Bootstrap, universality and horizons journal October 2016
Analytic continuation of Liouville theory journal December 2011
Modular bootstrap revisited journal September 2018
A cardy formula for three-point coefficients or how the black hole got its spots journal May 2017
Exact Virasoro blocks from Wilson lines and background-independent operators journal July 2017
On the Polyakov-Mellin bootstrap journal December 2018
Causality constraints on corrections to the graviton three-point coupling journal February 2016
Light-ray operators in conformal field theory journal November 2018
Universal anomalous dimensions at large spin and large twist journal July 2015
A conformal block Farey tail journal June 2017
A tauberian theorem for the conformal bootstrap journal December 2017
Bekenstein-Hawking entropy as topological entanglement entropy journal November 2013
Liouville theory revisited journal November 2001
On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles journal April 2017
On modular transformations of toric conformal blocks journal October 2015
Resummation at finite conformal spin journal January 2019
Conformal collider physics: energy and charge correlations journal May 2008
Small black holes and near-extremal CFTs journal August 2016
A spacetime derivation of the Lorentzian OPE inversion formula journal July 2018
Holography from conformal field theory journal October 2009
Analytic bootstrap at large spin journal November 2015
Conformal Field Theory Interpretation of Black Hole Quasinormal Modes journal March 2002
Large Spin Perturbation Theory for Conformal Field Theories journal September 2017
Universality of long-distance AdS physics from the CFT bootstrap journal August 2014
Eikonal approximation in AdS/CFT: from shock waves to four-point functions journal August 2007
Closure of the operator product expansion in the non-unitary bootstrap journal November 2016
Late time Wilson lines journal April 2019
Probing beyond ETH at large c journal June 2018
Convexity and liberation at large spin journal November 2013
A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance journal October 2017
Charged structure constants from modularity journal November 2017
Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion journal September 2007
Heavy-heavy-light-light correlators in Liouville theory journal August 2017
Emergent spacetime and holographic CFTs journal October 2012
Effective conformal theory and the flat-space limit of AdS journal July 2011
Recent Progress in Liouville Field Theory (Review) journal May 2004
Witten diagrams revisited: the AdS geometry of conformal blocks journal January 2016
Unitarity and the holographic S-Matrix journal October 2012
Chaos and quantum thermalization journal August 1994
The lightcone bootstrap and the spectrum of the 3d Ising CFT journal March 2017
d-dimensional SYK, AdS loops, and 6j symbols journal March 2019
Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ)) journal December 2001
Two- and three-point functions in Liouville theory journal October 1994
Conformal bootstrap in Liouville field theory journal October 1996
Conformal bootstrap, universality and gravitational scattering journal December 2015
Bootstrapping 2D CFTs in the semiclassical limit journal August 2016
Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs journal January 2019
Positivity constraints for anomalous dimensions journal October 1973
Universal asymptotics of three-point coefficients from elliptic representation of Virasoro blocks journal November 2018
Analytic properties of the Virasoro modular kernel journal June 2017
Polynomial equations for rational conformal field theories journal October 1988
Operator content of two-dimensional conformally invariant theories journal January 1986
Poincaré series, 3D gravity and CFT spectroscopy journal February 2015
Correlators in higher-spin AdS3 holography from Wilson lines with loop corrections journal November 2017
A theory of reparameterizations for AdS3 gravity journal February 2019
Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity journal January 2019
6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories journal February 2014
Infinite conformal symmetry in two-dimensional quantum field theory journal July 1984
N $$ \mathcal{N} $$ = 4 superconformal bootstrap of the K3 CFT journal May 2017
Renyi entropy for local quenches in 2D CFT from numerical conformal blocks journal January 2018
Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions journal April 2007
Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling journal December 2018
Loop Corrections to Supergravity on AdS 5 × S 5 journal October 2017
Constraints on higher spin CFT2 journal May 2018
Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude journal September 1984
Graviton exchange and complete four-point functions in the AdS/CFT correspondence journal November 1999
Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks journal July 2015
2D CFT partition functions at late times journal August 2017
On the Barnes double zeta and Gamma functions journal September 2009
Entanglement scrambling in 2d conformal field theory journal September 2015
Holography from Conformal Field Theory text January 2009
Effective Conformal Theory and the Flat-Space Limit of AdS text January 2010
Emergent Spacetime and Holographic CFTs text January 2011
Universality of Long-Distance AdS Physics from the CFT Bootstrap text January 2014
Virasoro Conformal Blocks and Thermality from Classical Background Fields text January 2015
Universal anomalous dimensions at large spin and large twist text January 2015
Higgsing the stringy higher spin symmetry preprint January 2015
Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks text January 2015
A conformal block Farey tail text January 2016
On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles text January 2016
Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators text January 2016
Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ text January 2017
Analyticity in Spin in Conformal Theories text January 2017
An Exact Operator That Knows Its Location text January 2017
New Properties of Large-$c$ Conformal Blocks from Recursion Relation text January 2018
Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications text January 2018
Light-ray operators in conformal field theory text January 2018
Anomalous dimensions at finite conformal spin from OPE inversion text January 2018
Anomalous Dimensions from Crossing Kernels text January 2018
Resummation at finite conformal spin text January 2018
Chaos and Quantum Thermalization text January 1994
Liouville theory revisited text January 2001
Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions text January 2006
Coupled Potts models: Self-duality and fixed point structure journal May 1999
Supersymmetric gauge theories, quantization of $\mathcal{M}_{\mathrm{flat}}$, and conformal field theory journal January 2015
Analytic properties of the Virasoro modular kernel text January 2016
From Liouville Theory to the Quantum Geometry of Riemann Surfaces preprint January 2003

Cited By (15)

Barrier from chaos: operator entanglement dynamics of the reduced density matrix journal December 2019
Entanglement Entropy after Double Excitation as an Interaction Measure journal February 2020
An inelastic bound on chaos journal July 2019
Bound on asymptotics of magnitude of three point coefficients in 2D CFT text January 2019
Entanglement Entropy after Double-Excitation as Interaction Measure text January 2019
The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy journal March 2021
The Virasoro fusion kernel and Ruijsenaars’ hypergeometric function journal January 2021
Quantum thermalization and Virasoro symmetry journal June 2020
Bounds on the density of states and the spectral gap in CFT$_{2}$ text January 2019
Aspects of the S transformation Bootstrap text January 2019
Beurling-Selberg Extremization and Modular Bootstrap at High Energies text January 2020
Confluent Conformal Blocks of the Second Kind text January 2020
Virasoro blocks at large exchange dimension text January 2020
Discreteness and Integrality in Conformal Field Theory text January 2020
Analytic Bootstrap for Perturbative Conformal Field Theories preprint January 2020

Similar Records

Holographic reconstruction of AdS exchanges from crossing symmetry
Journal Article · Thu Aug 31 00:00:00 EDT 2017 · Journal of High Energy Physics (Online) · OSTI ID:1611635
Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
Journal Article · Thu Nov 12 00:00:00 EST 2020 · Journal of High Energy Physics (Online) · OSTI ID:1611635
+2 more
On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles
Journal Article · Wed Apr 12 00:00:00 EDT 2017 · Journal of High Energy Physics (Online) · OSTI ID:1611635

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Physics
AdS-CFT Correspondence
Conformal Field Theory
Gauge-gravity correspondence