Displacement Operators and Constraints on Boundary Central Charges

Herzog, Christopher; Huang, Kuo-Wei; Jensen, Kristan

doi:10.1103/PhysRevLett.120.021601

Title: Displacement Operators and Constraints on Boundary Central Charges

Abstract

Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. Moreover, we conjecture a relation between the α-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.

Authors:: Herzog, Christopher; Huang, Kuo-Wei; Jensen, Kristan

Publication Date:: Mon Jan 08 00:00:00 EST 2018

Research Org.:: San Francisco State Univ., San Francisco, CA (United States)

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

OSTI Identifier:: 1416067

Alternate Identifier(s):: OSTI ID: 1501845

Grant/Contract Number:: SC0013682

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 120 Journal Issue: 2; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Herzog, Christopher, Huang, Kuo-Wei, and Jensen, Kristan. Displacement Operators and Constraints on Boundary Central Charges.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevLett.120.021601.

Copy to clipboard


                    Herzog, Christopher, Huang, Kuo-Wei, & Jensen, Kristan. Displacement Operators and Constraints on Boundary Central Charges.  United States.  https://doi.org/10.1103/PhysRevLett.120.021601

Copy to clipboard


                    Herzog, Christopher, Huang, Kuo-Wei, and Jensen, Kristan. Mon .  
"Displacement Operators and Constraints on Boundary Central Charges".  United States.  https://doi.org/10.1103/PhysRevLett.120.021601.

Copy to clipboard


                    
@article{osti_1416067,

  title        = {Displacement Operators and Constraints on Boundary Central Charges},

  author       = {Herzog, Christopher and Huang, Kuo-Wei and Jensen, Kristan},

  abstractNote = {Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. Moreover, we conjecture a relation between the α-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.},

  doi          = {10.1103/PhysRevLett.120.021601},

  journal      = {Physical Review Letters},

  number       = 2,

  volume       = 120,

  place        = {United States},

  year         = {Mon Jan 08 00:00:00 EST 2018},

  month        = {Mon Jan 08 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevLett.120.021601

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 40 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
journal, March 2016

Bzowski, Adam; McFadden, Paul; Skenderis, Kostas
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)066

Boundary terms in the heat kernel expansion
journal, May 1989

Moss, I. G.
Classical and Quantum Gravity, Vol. 6, Issue 5
DOI: 10.1088/0264-9381/6/5/017

A finite entanglement entropy and the c-theorem
journal, October 2004

Casini, H.; Huerta, M.
Physics Letters B, Vol. 600, Issue 1-2
DOI: 10.1016/j.physletb.2004.08.072

Conformal invariance and the regularised one-loop effective action
journal, December 1988

Melmed, J.
Journal of Physics A: Mathematical and General, Vol. 21, Issue 23
DOI: 10.1088/0305-4470/21/23/005

Geometric classification of conformal anomalies in arbitrary dimensions
journal, July 1993

Deser, S.; Schwimmer, A.
Physics Letters B, Vol. 309, Issue 3-4
DOI: 10.1016/0370-2693(93)90934-A

Constraint on Defect and Boundary Renormalization Group Flows
journal, March 2016

Jensen, Kristan; O’Bannon, Andy
Physical Review Letters, Vol. 116, Issue 9
DOI: 10.1103/PhysRevLett.116.091601

Relative entropy and the Bekenstein bound
journal, September 2008

Casini, H.
Classical and Quantum Gravity, Vol. 25, Issue 20
DOI: 10.1088/0264-9381/25/20/205021

Conformal field theories near a boundary in general dimensions
journal, September 1995

McAvity, D. M.; Osborn, H.
Nuclear Physics B, Vol. 455, Issue 3
DOI: 10.1016/0550-3213(95)00476-9

Renormalization group running of the entanglement entropy of a circle
journal, June 2012

Casini, H.; Huerta, M.
Physical Review D, Vol. 85, Issue 12
DOI: 10.1103/PhysRevD.85.125016

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

Conformal anomalies of CFT’s with boundaries
journal, December 2015

Fursaev, D. V.
Journal of High Energy Physics, Vol. 2015, Issue 12
DOI: 10.1007/JHEP12(2015)112

Boundary terms of conformal anomaly
journal, January 2016

Solodukhin, Sergey N.
Physics Letters B, Vol. 752
DOI: 10.1016/j.physletb.2015.11.036

Conformal anomaly of submanifold observables in AdS/CFT correspondence
journal, April 1999

Robin Graham, C.; Witten, Edward
Nuclear Physics B, Vol. 546, Issue 1-2
DOI: 10.1016/S0550-3213(99)00055-3

Differential regularization and renormalization: a new method of calculation in quantum field theory
journal, March 1992

Freedman, Daniel Z.; Johnson, Kenneth; Latorre, JoséI.
Nuclear Physics B, Vol. 371, Issue 1-2
DOI: 10.1016/0550-3213(92)90240-C

Conformal collider physics: energy and charge correlations
journal, May 2008

Hofman, Diego M.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2008, Issue 05
DOI: 10.1088/1126-6708/2008/05/012

Boundary conformal field theory and a boundary central charge
journal, October 2017

Herzog, Christopher P.; Huang, Kuo-Wei
Journal of High Energy Physics, Vol. 2017, Issue 10
DOI: 10.1007/JHEP10(2017)189

Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories
journal, October 1991

Osborn, H.
Nuclear Physics B, Vol. 363, Issue 2-3
DOI: 10.1016/0550-3213(91)80030-P

Markov Property of the Conformal Field Theory Vacuum and the $a$ Theorem
journal, June 2017

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
Physical Review Letters, Vol. 118, Issue 26
DOI: 10.1103/PhysRevLett.118.261602

Universal entanglement and boundary geometry in conformal field theory
journal, January 2016

Herzog, Christopher P.; Huang, Kuo-Wei; Jensen, Kristan
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)162

Central charges for BCFTs and holography
journal, June 2012

Nozaki, Masahiro; Takayanagi, Tadashi; Ugajin, Tomonori
Journal of High Energy Physics, Vol. 2012, Issue 6
DOI: 10.1007/JHEP06(2012)066

Anomalies, entropy, and boundaries
journal, April 2016

Fursaev, Dmitry V.; Solodukhin, Sergey N.
Physical Review D, Vol. 93, Issue 8
DOI: 10.1103/PhysRevD.93.084021

Implications of conformal invariance in momentum space
journal, March 2014

Bzowski, Adam; McFadden, Paul; Skenderis, Kostas
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)111

Energy-momentum tensor in conformal field theories near a boundary
journal, October 1993

McAvity, D. M.; Osborn, H.
Nuclear Physics B, Vol. 406, Issue 3
DOI: 10.1016/0550-3213(93)90005-A

Rényi entropy and conformal defects
journal, July 2016

Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.
Journal of High Energy Physics, Vol. 2016, Issue 7
DOI: 10.1007/JHEP07(2016)076

Similar Records in DOE PAGES and OSTI.GOV collections:

$$\mathcal{N}$$ = (1, 0) anomaly multiplet relations in six dimensions

Journal Article Córdova, Clay ; Dumitrescu, Thomas T. ; Intriligator, Kenneth - Journal of High Energy Physics (Online)

We consider conformal and ’t Hooft anomalies in six-dimensionalmore »« less
Cited by 8
https://doi.org/10.1007/JHEP07(2020)065

Full Text Available
Einstein gravity 3-point functions from conformal field theory

Journal Article Afkhami-Jeddi, Nima ; Hartman, Thomas ; Kundu, Sandipan ; ... - Journal of High Energy Physics (Online)

We report on stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter implies that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functionsmore »« less
Cited by 67
https://doi.org/10.1007/jhep12(2017)049

Full Text Available
TTT in CFT: Trace identities and the conformal anomaly effective action

Journal Article Corianò, Claudio ; Maglio, Matteo Maria ; Mottola, Emil - Nuclear Physics. B

Stress-energy correlation functions in a general Conformal Field Theory (CFT) in four dimensions are described in a fully covariant approach, as metric variations of the quantum effective action in an arbitrary curved space background field. All Conservation, Trace and Conformal Ward Identities (CWIs), including contact terms, are completely fixed in this covariant approach. The Trace and CWIs are anomalous. Their anomalous contributions may be computed unambiguously by metric variation of the exact 1PI quantum effective action determined by the conformal anomaly ofmore »« less
Cited by 21
https://doi.org/10.1016/j.nuclphysb.2019.03.019

Full Text Available
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 34
https://doi.org/10.1007/jhep08(2019)138

Full Text Available
Central charge bounds in 4D conformal field theory

Journal Article Rattazzi, Riccardo ; Vichi, Alessandro ; Rychkov, Slava - Physical Review. D, Particles Fields

We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.
https://doi.org/10.1103/PHYSREVD.83.046011

Similar Records

Title: Displacement Operators and Constraints on Boundary Central Charges

Abstract

Citation Formats

Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies journal, March 2016

Boundary terms in the heat kernel expansion journal, May 1989

A finite entanglement entropy and the c-theorem journal, October 2004

Conformal invariance and the regularised one-loop effective action journal, December 1988

Geometric classification of conformal anomalies in arbitrary dimensions journal, July 1993

Constraint on Defect and Boundary Renormalization Group Flows journal, March 2016

Relative entropy and the Bekenstein bound journal, September 2008

Conformal field theories near a boundary in general dimensions journal, September 1995

Renormalization group running of the entanglement entropy of a circle journal, June 2012

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

Conformal anomalies of CFT’s with boundaries journal, December 2015

Boundary terms of conformal anomaly journal, January 2016

Conformal anomaly of submanifold observables in AdS/CFT correspondence journal, April 1999

Differential regularization and renormalization: a new method of calculation in quantum field theory journal, March 1992

Conformal collider physics: energy and charge correlations journal, May 2008

Boundary conformal field theory and a boundary central charge journal, October 2017

Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories journal, October 1991

Markov Property of the Conformal Field Theory Vacuum and the a Theorem journal, June 2017

Universal entanglement and boundary geometry in conformal field theory journal, January 2016

Central charges for BCFTs and holography journal, June 2012

Anomalies, entropy, and boundaries journal, April 2016

Implications of conformal invariance in momentum space journal, March 2014

Energy-momentum tensor in conformal field theories near a boundary journal, October 1993

Rényi entropy and conformal defects journal, July 2016

Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
journal, March 2016

Boundary terms in the heat kernel expansion
journal, May 1989

A finite entanglement entropy and the c-theorem
journal, October 2004

Conformal invariance and the regularised one-loop effective action
journal, December 1988

Geometric classification of conformal anomalies in arbitrary dimensions
journal, July 1993

Constraint on Defect and Boundary Renormalization Group Flows
journal, March 2016

Relative entropy and the Bekenstein bound
journal, September 2008

Conformal field theories near a boundary in general dimensions
journal, September 1995

Renormalization group running of the entanglement entropy of a circle
journal, June 2012

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

Conformal anomalies of CFT’s with boundaries
journal, December 2015

Boundary terms of conformal anomaly
journal, January 2016

Conformal anomaly of submanifold observables in AdS/CFT correspondence
journal, April 1999

Differential regularization and renormalization: a new method of calculation in quantum field theory
journal, March 1992

Conformal collider physics: energy and charge correlations
journal, May 2008

Boundary conformal field theory and a boundary central charge
journal, October 2017

Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories
journal, October 1991

Markov Property of the Conformal Field Theory Vacuum and the $a$ Theorem
journal, June 2017

Universal entanglement and boundary geometry in conformal field theory
journal, January 2016

Central charges for BCFTs and holography
journal, June 2012

Anomalies, entropy, and boundaries
journal, April 2016

Implications of conformal invariance in momentum space
journal, March 2014

Energy-momentum tensor in conformal field theories near a boundary
journal, October 1993

Rényi entropy and conformal defects
journal, July 2016