From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects

Jensen, Kristan; O’Bannon, Andy; Robinson, Brandon; Rodgers, Ronnie

doi:10.1103/PhysRevLett.122.241602

Title: From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects

Journal Article · Wed Jun 19 00:00:00 EDT 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.122.241602· OSTI ID:1527054

Jensen, Kristan; O’Bannon, Andy; Robinson, Brandon; Rodgers, Ronnie

We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of D ≥ 3 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, b, obeys a c theorem, as in 2D CFT. For a 2D defect, we show that another, d₂, interpreted as the defect’s “conformal dimension,” must be non-negative if the averaged null energy condition holds in the presence of the defect. We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by b and d₂. Using this and known holographic results, we compute b and d₂ for 1/2-Bogomol’nyi-Prasad-Sommerfield surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with b’s c theorem. Via free field and holographic examples we show that no universal “Cardy formula” relates the central charges to thermal entropy.

View Journal Article

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0013682

OSTI ID:: 1527054

Alternate ID(s):: OSTI ID: 1612020

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Vol. 122 Journal Issue: 24; ISSN 0031-9007

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 29 works

Citation information provided by
Web of Science

References (53)

Weyl cocycles Bonora, L.; Pasti, P.; Bregola, M. Classical and Quantum Gravity, Vol. 3, Issue 4 https://doi.org/10.1088/0264-9381/3/4/018	journal	July 1986
Anti-de Sitter space, thermal phase transition, and confinement in gauge theories Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3 https://doi.org/10.4310/ATMP.1998.v2.n3.a3	journal	January 1998
On holographic defect entropy Estes, John; Jensen, Kristan; O’Bannon, Andy Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)084	journal	May 2014
1/2-BPS states in M theory and defects in the dual CFTs Lunin, Oleg Journal of High Energy Physics, Vol. 2007, Issue 10 https://doi.org/10.1088/1126-6708/2007/10/014	journal	October 2007
Geometric classification of conformal anomalies in arbitrary dimensions Deser, S.; Schwimmer, A. Physics Letters B, Vol. 309, Issue 3-4 https://doi.org/10.1016/0370-2693(93)90934-A	journal	July 1993
Constraint on Defect and Boundary Renormalization Group Flows Jensen, Kristan; O’Bannon, Andy Physical Review Letters, Vol. 116, Issue 9 https://doi.org/10.1103/PhysRevLett.116.091601	journal	March 2016
Fermions on an interval: Quark and lepton masses without a Higgs Csáki, Csaba; Grojean, Christophe; Hubisz, Jay Physical Review D, Vol. 70, Issue 1 https://doi.org/10.1103/PhysRevD.70.015012	journal	July 2004
Conformal field theories near a boundary in general dimensions McAvity, D. M.; Osborn, H. Nuclear Physics B, Vol. 455, Issue 3 https://doi.org/10.1016/0550-3213(95)00476-9	journal	September 1995
Twenty years of the Weyl anomaly Duff, M. J. Classical and Quantum Gravity, Vol. 11, Issue 6 https://doi.org/10.1088/0264-9381/11/6/004	journal	June 1994
Central Charges and the Sign of Entanglement in 4D Conformal Field Theories Perlmutter, Eric; Rangamani, Mukund; Rota, Massimiliano Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.171601	journal	October 2015
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)036	journal	May 2011
Holography, entanglement entropy, and conformal field theories with boundaries or defects Jensen, Kristan; O’Bannon, Andy Physical Review D, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevD.88.106006	journal	November 2013
Conformal invariance and universality in finite-size scaling Cardy, J. L. Journal of Physics A: Mathematical and General, Vol. 17, Issue 7 https://doi.org/10.1088/0305-4470/17/7/003	journal	May 1984
Partition functions and Casimir energies in higher spin ${AdS}_{d + 1} / {CFT}_{d}$ Giombi, Simone; Klebanov, Igor R.; Tseytlin, Arkady A. Physical Review D, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevD.90.024048	journal	July 2014
Probing 𝒩 = 4 SYM with surface operators Drukker, Nadav; Gomis, Jaume; Matsuura, Shunji Journal of High Energy Physics, Vol. 2008, Issue 10 https://doi.org/10.1088/1126-6708/2008/10/048	journal	October 2008
Displacement Operators and Constraints on Boundary Central Charges Herzog, Christopher; Huang, Kuo-Wei; Jensen, Kristan Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.021601	journal	January 2018
The large $N$ limit of superconformal field theories and supergravity Maldacena, Juan Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a1	journal	January 1998
Wilson surface central charge from holographic entanglement entropy Estes, John; Krym, Darya; O’Bannon, Andy Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/JHEP05(2019)032	journal	May 2019
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)038	journal	September 2016
Bubbling surface operators and S-duality Gomis, Jaume; Matsuura, Shunji Journal of High Energy Physics, Vol. 2007, Issue 06 https://doi.org/10.1088/1126-6708/2007/06/025	journal	June 2007
Entanglement entropy, trace anomalies and holography Schwimmer, A.; Theisen, S. Nuclear Physics B, Vol. 801, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2008.04.015	journal	September 2008
Localized modes at a D-brane—O-plane intersection and heterotic Alice strings Harvey, Jeffrey A.; Royston, Andrew B. Journal of High Energy Physics, Vol. 2008, Issue 04 https://doi.org/10.1088/1126-6708/2008/04/018	journal	April 2008
Six-dimensional tensionless strings in the large N limit Ganor, Ori J. Nuclear Physics B, Vol. 489, Issue 1-2 https://doi.org/10.1016/S0550-3213(96)00702-X	journal	March 1997
Boundary conformal field theory and a boundary central charge Herzog, Christopher P.; Huang, Kuo-Wei Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)189	journal	October 2017
Gauge/gravity duality with a chiral 𝒩 = (0, 8) string defect Harvey, Jeffrey A.; Royston, Andrew B. Journal of High Energy Physics, Vol. 2008, Issue 08 https://doi.org/10.1088/1126-6708/2008/08/006	journal	August 2008
Holographic entanglement entropy from probe M-theory branes Rodgers, Ronnie Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)092	journal	March 2019
M5-branes and Wilson surfaces Chen, Bin; Zhang, Liang; He, Wei Journal of High Energy Physics, Vol. 2007, Issue 08 https://doi.org/10.1088/1126-6708/2007/08/067	journal	August 2007
Universal term in the free energy at a critical point and the conformal anomaly Affleck, Ian Physical Review Letters, Vol. 56, Issue 7 https://doi.org/10.1103/PhysRevLett.56.746	journal	February 1986
Central charges for BCFTs and holography Nozaki, Masahiro; Takayanagi, Tadashi; Ugajin, Tomonori Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)066	journal	June 2012
Vortex loop operators, M2-branes and holography Drukker, Nadav; Gomis, Jaume; Young, Donovan Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/004	journal	March 2009
M-theory solutions invariant under D(2,1; γ) ⊕ D(2,1;γ) Bachas, C.; D'Hoker, E.; Estes, J. Fortschritte der Physik, Vol. 62, Issue 3 https://doi.org/10.1002/prop.201300039	journal	February 2014
Consequences of anomalous ward identities Wess, J.; Zumino, B. Physics Letters B, Vol. 37, Issue 1 https://doi.org/10.1016/0370-2693(71)90582-X	journal	November 1971
Holographic gauge theories in background fields and surface operators Buchbinder, Evgeny I.; Gomis, Jaume; Passerini, Filippo Journal of High Energy Physics, Vol. 2007, Issue 12 https://doi.org/10.1088/1126-6708/2007/12/101	journal	December 2007
Towards a C-theorem in defect CFT Kobayashi, Nozomu; Nishioka, Tatsuma; Sato, Yoshiki Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/JHEP01(2019)039	journal	January 2019
Exact half-BPS flux solutions in M-theory II: global solutions asymptotic to AdS ₇ × S ⁴ D'Hoker, Eric; Estes, John; Gutperle, Michael Journal of High Energy Physics, Vol. 2008, Issue 12 https://doi.org/10.1088/1126-6708/2008/12/044	journal	December 2008
Operator content of two-dimensional conformally invariant theories Cardy, John L. Nuclear Physics B, Vol. 270 https://doi.org/10.1016/0550-3213(86)90552-3	journal	January 1986
Conformal anomaly of submanifold observables in AdS/CFT correspondence Robin Graham, C.; Witten, Edward Nuclear Physics B, Vol. 546, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00055-3	journal	April 1999
Averaged null energy condition from causality Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)066	journal	July 2017
Supersymmetric baryonic branes Gomis, Joaquim; Simón, Joan; Ramallo, Alfonso V. Journal of High Energy Physics, Vol. 1999, Issue 11 https://doi.org/10.1088/1126-6708/1999/11/019	journal	November 1999
Geometric and renormalized entropy in conformal field theory Holzhey, Christoph; Larsen, Finn; Wilczek, Frank Nuclear Physics B, Vol. 424, Issue 3 https://doi.org/10.1016/0550-3213(94)90402-2	journal	August 1994
M5-branes and Wilson surfaces in the ${AdS}_{7} / {CFT}_{6}$ correspondence Mori, Hironori; Yamaguchi, Satoshi Physical Review D, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevD.90.026005	journal	July 2014
Holographic entanglement entropy of surface defects Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos Journal of High Energy Physics, Vol. 2016, Issue 4 https://doi.org/10.1007/JHEP04(2016)067	journal	April 2016
Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)019	journal	August 2015
Universality in the geometric dependence of Rényi entropy Lewkowycz, Aitor; Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)080	journal	January 2015
Physics at the entangling surface Ohmori, Kantaro; Tachikawa, Yuji Journal of Statistical Mechanics: Theory and Experiment, Vol. 2015, Issue 4 https://doi.org/10.1088/1742-5468/2015/04/P04010	journal	April 2015
Entanglement of heavy quark impurities and generalized gravitational entropy Kumar, S. Prem; Silvani, Dorian Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)052	journal	January 2018
Stable wrapped branes Camino, Jose M.; Paredes, Angel; Ramallo, Alfonso V. Journal of High Energy Physics, Vol. 2001, Issue 05 https://doi.org/10.1088/1126-6708/2001/05/011	journal	May 2001
Entanglement entropy and quantum field theory Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2004, Issue 06 https://doi.org/10.1088/1742-5468/2004/06/P06002	journal	June 2004
Anomalies, entropy, and boundaries Fursaev, Dmitry V.; Solodukhin, Sergey N. Physical Review D, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevD.93.084021	journal	April 2016
Wilson-’t Hooft operators in four-dimensional gauge theories and $S$ -duality Kapustin, Anton Physical Review D, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevD.74.025005	journal	July 2006
Energy-momentum tensor in conformal field theories near a boundary McAvity, D. M.; Osborn, H. Nuclear Physics B, Vol. 406, Issue 3 https://doi.org/10.1016/0550-3213(93)90005-A	journal	October 1993
Rényi entropy and conformal defects Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C. Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)076	journal	July 2016
Weyl anomaly for Wilson surfaces Henningson, Måns; Skenderis, Kostas Journal of High Energy Physics, Vol. 1999, Issue 06 https://doi.org/10.1088/1126-6708/1999/06/012	journal	June 1999

Similar Records

Nearing 11D extremal intersecting giants and new decoupled sectors in D=3, 6 superconformal field theories

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields · OSTI ID:1527054

Fareghbal, R; Gowdigere, C N; Mosaffa, A E; +1 more

New massive gravity extended with an arbitrary number of curvature corrections

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields · OSTI ID:1527054

Paulos, Miguel F

The Kerr/CFT correspondence

Journal Article · Tue Dec 15 00:00:00 EST 2009 · Physical Review. D, Particles Fields · OSTI ID:1527054

Guica, Monica; Hartman, Thomas; Wei, Song; +1 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Anomalies
Conformal field theory
Weyl fermions

Title: From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects

Citation Formats

References (53)

Similar Records

Related Subjects