Stress-tensor commutators in conformal field theories near the lightcone

Huang, Kuo-Wei

doi:10.1103/PhysRevD.100.061701

Title: Stress-tensor commutators in conformal field theories near the lightcone

Abstract

Starting with the general stress-tensor commutation relations consistent with the Poincaré algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in d > 2 conformal field theories.

Authors:: Huang, Kuo-Wei

Publication Date:: 2019-09-17

Research Org.:: Boston Univ., MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1562326

Alternate Identifier(s):: OSTI ID: 1612336

Grant/Contract Number:: SC0015845

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 6; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics; Conformal field theory

Citation Formats


                    Huang, Kuo-Wei. Stress-tensor commutators in conformal field theories near the lightcone.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.061701.

Copy to clipboard


                    Huang, Kuo-Wei. Stress-tensor commutators in conformal field theories near the lightcone.  United States.  https://doi.org/10.1103/PhysRevD.100.061701

Copy to clipboard


                    Huang, Kuo-Wei. Tue .  
"Stress-tensor commutators in conformal field theories near the lightcone".  United States.  https://doi.org/10.1103/PhysRevD.100.061701.

Copy to clipboard


                    
@article{osti_1562326,

  title        = {Stress-tensor commutators in conformal field theories near the lightcone},

  author       = {Huang, Kuo-Wei},

  abstractNote = {Starting with the general stress-tensor commutation relations consistent with the Poincaré algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in d > 2 conformal field theories.},

  doi          = {10.1103/PhysRevD.100.061701},

  journal      = {Physical Review D},

  number       = 6,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.100.061701

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Energy and Momentum Density in Field Theory
journal, April 1963

Schwinger, Julian
Physical Review, Vol. 130, Issue 2
DOI: 10.1103/PhysRev.130.800

Anti de Sitter space and holography
journal, January 1998

Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
DOI: 10.4310/ATMP.1998.v2.n2.a2

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36
DOI: 10.1088/1751-8121/aa7eaa

Subsidiary Conditions and Ghosts in Dual-Resonance Models
journal, May 1970

Virasoro, M. A.
Physical Review D, Vol. 1, Issue 10
DOI: 10.1103/PhysRevD.1.2933

Non-Abelian Gauge Fields. Relativistic Invariance
journal, July 1962

Schwinger, Julian
Physical Review, Vol. 127, Issue 1
DOI: 10.1103/PhysRev.127.324

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Osborn, H.; Petkou, A.
Annals of Physics, Vol. 231, Issue 2
DOI: 10.1006/aphy.1994.1045

c -theorem and spectral representation
journal, April 1991

Cappelli, Andrea; Friedan, Daniel; Latorre, JoséI.
Nuclear Physics B, Vol. 352, Issue 3
DOI: 10.1016/0550-3213(91)90102-4

Shockwaves from the operator product expansion
journal, March 2019

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/JHEP03(2019)201

Correlation functions of the energy–momentum tensor on spaces of constant curvature
journal, April 2000

Osborn, H.; Shore, G. M.
Nuclear Physics B, Vol. 571, Issue 1-2
DOI: 10.1016/S0550-3213(99)00775-0

Light-ray operators and the BMS algebra
journal, December 2018

Córdova, Clay; Shao, Shu-Heng
Physical Review D, Vol. 98, Issue 12
DOI: 10.1103/PhysRevD.98.125015

Universal lowest-twist in CFTs from holography
journal, August 2019

Fitzpatrick, A. Liam; Huang, Kuo-Wei
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/JHEP08(2019)138

Stress-tensor commutation relations
journal, July 1970

Trubatch, J.
Il Nuovo Cimento A, Vol. 68, Issue 2
DOI: 10.1007/BF02754155

Stress‐Tensor Commutators and Schwinger Terms
journal, July 1967

Boulware, David G.; Deser, S.
Journal of Mathematical Physics, Vol. 8, Issue 7
DOI: 10.1063/1.1705368

Gauge theory correlators from non-critical string theory
journal, May 1998

Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
Physics Letters B, Vol. 428, Issue 1-2
DOI: 10.1016/S0370-2693(98)00377-3

Schwinger Terms in Stress-Tensor Commutators
journal, May 1969

Mahanthappa, K. T.
Physical Review, Vol. 181, Issue 5
DOI: 10.1103/PhysRev.181.2087

Approach to Equal-Time Commutators in Quantum Field Theory
journal, February 1968

Brandt, Richard A.
Physical Review, Vol. 166, Issue 5
DOI: 10.1103/PhysRev.166.1795

Anisotropic corrections to correlation functions in finite-size systems
journal, January 1987

Cardy, John L.
Nuclear Physics B, Vol. 290
DOI: 10.1016/0550-3213(87)90192-1

Similar Records in DOE PAGES and OSTI.GOV collections:

Lightcone commutator and stress-tensor exchange in $d > 2$ conformal field theories

Journal Article Huang, Kuo-Wei - Physical Review D

Motivated by developing a field-theoretic algebraic approach to the universal part of the stress-tensor sector of a scalar four-point function in a class of higher-dimensional conformal field theories (CFTs), we construct a mode operator,more »« less
https://doi.org/10.1103/PhysRevD.102.021701
$d > 2$ stress-tensor operator product expansion near a line

Journal Article Huang, Kuo-Wei - Physical Review D

We study the operator product expansion of stress tensors (TT OPE) in d > 2 conformal field theories whose bulk dual is Einstein gravity. Directly from the TT OPE, we obtain, in a certain null-like limit, an algebraic structure consistent with the Jacobi identity: [L_m, L_n] = (m – n)L_m+n + Cm(m² – 1) δ_m+n,0 . The dimensionless constant C is proportional to the central charge C_T. Transverse integrals in the definition of L_m play a crucial role. We comment on the corresponding limiting procedure and point out a curiosity related to the central term. A connection between the dmore »« less
https://doi.org/10.1103/PhysRevD.103.L121702
Conformal field theories with infinitely many conservation laws

Journal Article Todorov, Ivan - Journal of Mathematical Physics

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys.more »« less
https://doi.org/10.1063/1.4790408
Universal lowest-twist in CFTs from holography

Journal Article Fitzpatrick, A. Liam ; Huang, Kuo-Wei - Journal of High Energy Physics (Online)

We probe the conformal block structure of a scalar four-point function in d ≥ 2 conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. Themore »« less
Cited by 10
https://doi.org/10.1007/jhep08(2019)138

Full Text Available
THE CONFORMAL INVARIANCE IN QUANTUM FIELD THEORY

Journal Article Wess, J - Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B

The properties of a conformal invariant quantum field theory are considered. A short discussion of the conformal group in four dimensions and of the topology, introduced into the pseudo-euclidean space by this group, is given. With the help of the commutation relations the spectrum of the generators in Hilbert-space is investigated. It is found that the only possible discrete eigenvalue of P/sup 2/ and of the P/sup v/'s is zero and that the generator for scale transformations S has a continuous spectrum. The eigenfunctions of S in the x-representation are calculated; they form a complete set. The conservation laws validmore »« less
https://doi.org/10.1007/BF02733168

Similar Records

Title: Stress-tensor commutators in conformal field theories near the lightcone

Abstract

Citation Formats

Energy and Momentum Density in Field Theory journal, April 1963

Anti de Sitter space and holography journal, January 1998

Modular Hamiltonians on the null plane and the Markov property of the vacuum state journal, August 2017

Subsidiary Conditions and Ghosts in Dual-Resonance Models journal, May 1970

Non-Abelian Gauge Fields. Relativistic Invariance journal, July 1962

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

c -theorem and spectral representation journal, April 1991

Shockwaves from the operator product expansion journal, March 2019

Correlation functions of the energy–momentum tensor on spaces of constant curvature journal, April 2000

Light-ray operators and the BMS algebra journal, December 2018

Universal lowest-twist in CFTs from holography journal, August 2019

Stress-tensor commutation relations journal, July 1970

Stress‐Tensor Commutators and Schwinger Terms journal, July 1967

Gauge theory correlators from non-critical string theory journal, May 1998

Schwinger Terms in Stress-Tensor Commutators journal, May 1969

Approach to Equal-Time Commutators in Quantum Field Theory journal, February 1968

Anisotropic corrections to correlation functions in finite-size systems journal, January 1987

Energy and Momentum Density in Field Theory
journal, April 1963

Anti de Sitter space and holography
journal, January 1998

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Subsidiary Conditions and Ghosts in Dual-Resonance Models
journal, May 1970

Non-Abelian Gauge Fields. Relativistic Invariance
journal, July 1962

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

c -theorem and spectral representation
journal, April 1991

Shockwaves from the operator product expansion
journal, March 2019

Correlation functions of the energy–momentum tensor on spaces of constant curvature
journal, April 2000

Light-ray operators and the BMS algebra
journal, December 2018

Universal lowest-twist in CFTs from holography
journal, August 2019

Stress-tensor commutation relations
journal, July 1970

Stress‐Tensor Commutators and Schwinger Terms
journal, July 1967

Gauge theory correlators from non-critical string theory
journal, May 1998

Schwinger Terms in Stress-Tensor Commutators
journal, May 1969

Approach to Equal-Time Commutators in Quantum Field Theory
journal, February 1968

Anisotropic corrections to correlation functions in finite-size systems
journal, January 1987