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

Title: Constraints on higher spin CFT 2

Abstract

We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with WN symmetry in the “irrational” regime, where c > N – 1 and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when c > N – 1. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large c, this implies that the dual holographic theories of gravity in AdS 3, if they exist, have no local, perturbative degrees of freedom in the semi-classical limit.

Authors:
ORCiD logo [1];  [2];  [1];  [2];  [3]
  1. Cornell Univ., Ithaca, NY (United States). Dept. of Physics
  2. McGill Univ., Montreal, QC (Canada). Dept of Physics
  3. Princeton Univ., Princeton, NJ (United States). Dept. of Physics
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1507425
Grant/Contract Number:  
FG02-91ER40671; PHY-160-7611
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Higher Spin Symmetry; Conformal Field Theory; Field Theories in Lower Dimensions; Higher Spin Gravity

Citation Formats

Afkhami-Jeddi, Nima, Colville, Kale, Hartman, Thomas, Maloney, Alexander, and Perlmutter, Eric. Constraints on higher spin CFT2. United States: N. p., 2018. Web. doi:10.1007/jhep05(2018)092.
Afkhami-Jeddi, Nima, Colville, Kale, Hartman, Thomas, Maloney, Alexander, & Perlmutter, Eric. Constraints on higher spin CFT2. United States. doi:10.1007/jhep05(2018)092.
Afkhami-Jeddi, Nima, Colville, Kale, Hartman, Thomas, Maloney, Alexander, and Perlmutter, Eric. Tue . "Constraints on higher spin CFT2". United States. doi:10.1007/jhep05(2018)092. https://www.osti.gov/servlets/purl/1507425.
@article{osti_1507425,
title = {Constraints on higher spin CFT2},
author = {Afkhami-Jeddi, Nima and Colville, Kale and Hartman, Thomas and Maloney, Alexander and Perlmutter, Eric},
abstractNote = {We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with WN symmetry in the “irrational” regime, where c > N – 1 and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when c > N – 1. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large c, this implies that the dual holographic theories of gravity in AdS3, if they exist, have no local, perturbative degrees of freedom in the semi-classical limit.},
doi = {10.1007/jhep05(2018)092},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2018,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Constraints on 2d CFT partition functions
journal, October 2013

  • Friedan, Daniel; Keller, Christoph A.
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)180

W-algebras with set of primary fields of dimensions (3, 4, 5) and (3, 4, 5, 6)
journal, October 1993


On sw Minimal Models and n = 1 Supersymmetric Quantum toda Field Theories
journal, March 1995


Modular invariant partition functions in two dimensions
journal, January 1987


A study of W-algebras using Jacobi identities
journal, May 1991


Causality constraints in conformal field theory
journal, May 2016

  • Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)099

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

  • Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)004

Extension of n = 2 Superconformal Algebra and Calabi-Yau Compactification
journal, March 1989


A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories
journal, November 1986


Higher spin black holes from CFT
journal, April 2012

  • Gaberdiel, Matthias R.; Hartman, Thomas; Jin, Kewang
  • Journal of High Energy Physics, Vol. 2012, Issue 4
  • DOI: 10.1007/JHEP04(2012)103

The complete structure of the nonlinear W4 and W5 algebras from the quantum Miura transformation
journal, October 1993


Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
journal, March 1990


The Kazhdan–Lusztig conjecture for W algebras
journal, July 1996

  • De Vos, Koos; van Driel, Peter
  • Journal of Mathematical Physics, Vol. 37, Issue 7
  • DOI: 10.1063/1.531584

Symmetries of holographic minimal models
journal, May 2011

  • Gaberdiel, Matthias R.; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)031

Higher spin theories in AdS3 and a gravitational exclusion principle
journal, January 2011

  • Castro, Alejandra; Lepage-Jutier, Arnaud; Maloney, Alexander
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)142

Bounding the space of holographic CFTs with chaos
journal, October 2016


The large central charge limit of conformal blocks
journal, February 2012

  • Fateev, Vladimir; Ribault, Sylvain
  • Journal of High Energy Physics, Vol. 2012, Issue 2
  • DOI: 10.1007/JHEP02(2012)001

The Topological G<sub>2</sub> String
journal, January 2008

  • de Boer, Jan; Naqvi, Asad; Shomer, Assaf
  • Advances in Theoretical and Mathematical Physics, Vol. 12, Issue 2
  • DOI: 10.4310/ATMP.2008.v12.n2.a2

Determinant formulae for extended algebras in two-dimensional conformal field theory
journal, November 1989


Bounds on operator dimensions in 2D conformal field theories
journal, May 2014

  • Qualls, Joshua D.; Shapere, Alfred D.
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)091

Modular properties of characters of the W3 algebra
journal, January 2016

  • Iles, Nicholas J.; Watts, Gérard M. T.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)089

Entanglement scrambling in 2d conformal field theory
journal, September 2015

  • Asplund, Curtis T.; Bernamonti, Alice; Galli, Federico
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)110

Non-unitarity theorem for the a type Wn algebra
journal, November 1989


Properties of partial-wave amplitudes in conformal invariant field theories
journal, April 1975

  • Ferrara, S.; Gatto, R.; Grillo, A. F.
  • Il Nuovo Cimento A, Vol. 26, Issue 3
  • DOI: 10.1007/BF02769009

Determinant formula and unitarity for the W3 algebra
journal, May 1989


On the Elliptic Genera of Manifolds of Spin(7) Holonomy
journal, December 2015

  • Benjamin, Nathan; Harrison, Sarah M.; Kachru, Shamit
  • Annales Henri Poincaré, Vol. 17, Issue 10
  • DOI: 10.1007/s00023-015-0454-5

-Algebras with two and three generators
journal, August 1991


Bounds on CFTs with W 3 algebras and AdS 3 higher spin theories
journal, October 2017


Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions
journal, March 2016


Operator content of two-dimensional conformally invariant theories
journal, January 1986


Universal spectrum of 2d conformal field theory in the large c limit
journal, September 2014

  • Hartman, Thomas; Keller, Christoph A.; Stoica, Bogdan
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)118

COSET REALIZATION OF UNIFYING ${\mathcal W}$ ALGEBRAS
journal, June 1995

  • Blumenhagen, R.; Eholzer, W.; Honecker, A.
  • International Journal of Modern Physics A, Vol. 10, Issue 16
  • DOI: 10.1142/S0217751X95001157

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

A MATHEMATICA ™ PACKAGE FOR COMPUTING OPERATOR PRODUCT EXPANSIONS
journal, September 1991


Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds of G 2 holonomy
journal, March 2002


A universal inequality for CFT and quantum gravity
journal, August 2011


W symmetry in conformal field theory
journal, February 1993


Correlation functions in holographic minimal models
journal, March 2012


Convexity and liberation at large spin
journal, November 2013

  • Komargodski, Zohar; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)140

c=3d CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY
journal, March 1990


The spectrum of light states in large N minimal models
journal, January 2014

  • Gaberdiel, Matthias R.; Gopakumar, Rajesh; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2014, Issue 1
  • DOI: 10.1007/JHEP01(2014)116

On the Uniqueness of Higher-Spin Symmetries in ads and cft
journal, December 2013

  • Boulanger, N.; Ponomarev, D.; Skvortsov, E.
  • International Journal of Modern Physics A, Vol. 28, Issue 31
  • DOI: 10.1142/S0217751X13501625

2 + 1 dimensional gravity as an exactly soluble system
journal, December 1988


Systematic Approach to Cyclic Orbifolds
journal, January 1998

  • Borisov, L.; Halpern, M. B.; Schweigert, C.
  • International Journal of Modern Physics A, Vol. 13, Issue 01
  • DOI: 10.1142/S0217751X98000044

Higher spin gravity with matter in AdS 3 and its CFT dual
journal, October 2012


Unitary representations of superconformal algebra
journal, September 2001


Infinite additional symmetries in two-dimensional conformal quantum field theory
journal, December 1985

  • Zamolodchikov, A. B.
  • Theoretical and Mathematical Physics, Vol. 65, Issue 3
  • DOI: 10.1007/BF01036128

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984


Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
journal, November 2010

  • Campoleoni, A.; Fredenhagen, S.; Pfenninger, S.
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)007

Universal bounds on charged states in 2d CFT and 3d gravity
journal, August 2016

  • Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)041

THE STRUCTURE OF REPRESENTATION FOR THE W (3) MINIMAL MODEL
journal, January 1991


Characters of the W 3 algebra
journal, February 2014

  • Iles, Nicholas J.; Watts, Gérard M. T.
  • Journal of High Energy Physics, Vol. 2014, Issue 2
  • DOI: 10.1007/JHEP02(2014)009