BRST cohomology is Lie algebroid cohomology

Jia, Weizhen; Klinger, Marc S.; Leigh, Robert G.

doi:10.1016/j.nuclphysb.2023.116317

Title: BRST cohomology is Lie algebroid cohomology

Journal Article · 31 August 2023 · Nuclear Physics. B

DOI: https://doi.org/10.1016/j.nuclphysb.2023.116317 · OSTI ID:1993658

; Klinger, Marc S.; Leigh, Robert G.

Not Available

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0015655

OSTI ID:: 1993658

Journal Information:: Nuclear Physics. B, Journal Name: Nuclear Physics. B Journal Issue: C Vol. 994; ISSN 0550-3213

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (59)

Lie Algebroids, Holonomy and Characteristic Classes Loja Fernandes, Rui Advances in Mathematics, Vol. 170, Issue 1 https://doi.org/10.1006/aima.2001.2070	journal	September 2002
Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations Bonora, L.; Cotta-Ramusino, P. Communications in Mathematical Physics, Vol. 87, Issue 4 https://doi.org/10.1007/BF01208267	journal	December 1983
Hamiltonian interpretation of anomalies Nelson, Philip; Alvarez-Gaumé, Luis Communications in Mathematical Physics, Vol. 99, Issue 1 https://doi.org/10.1007/BF01466595	journal	March 1985
Weil algebra structure and geometrical meaning of BRST transformation in topological quantum field theory Kanno, H. Zeitschrift f�r Physik C Particles and Fields, Vol. 43, Issue 3 https://doi.org/10.1007/BF01506544	journal	September 1989
Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories Sorella, Silvio P. Communications in Mathematical Physics, Vol. 157, Issue 2 https://doi.org/10.1007/BF02099759	journal	October 1993
Explicit classical construction of the Faddeev-Popov ghost field Thierry-Mieg, J. Il Nuovo Cimento A, Vol. 56, Issue 4 https://doi.org/10.1007/BF02732091	journal	April 1980
Extended BRS symmetry in non-Abelian gauge theories Bonora, L.; Pasti, P.; Tonin, M. Il Nuovo Cimento A, Vol. 64, Issue 3 https://doi.org/10.1007/BF02812376	journal	August 1981
A PCAC puzzle: π0→γγ in the σ-model Bell, J. S.; Jackiw, R. Il Nuovo Cimento A, Vol. 60, Issue 1 https://doi.org/10.1007/BF02823296	journal	March 1969
Local BRST Cohomology and Covariance Brandt, Friedemann Communications in Mathematical Physics, Vol. 190, Issue 2 https://doi.org/10.1007/s002200050248	journal	December 1997
Forces Unification in the Framework of Transitive Lie Algebroids Ramandi, Gh. Fasihi; Boroojerdian, N. International Journal of Theoretical Physics, Vol. 54, Issue 5 https://doi.org/10.1007/s10773-014-2357-5	journal	October 2014
Renormalization of gauge theories Becchi, C.; Rouet, A.; Stora, R. Annals of Physics, Vol. 98, Issue 2 https://doi.org/10.1016/0003-4916(76)90156-1	journal	June 1976
Duality theorems in BRST cohomology Henneaux, Marc Annals of Physics, Vol. 194, Issue 2 https://doi.org/10.1016/0003-4916(89)90274-1	journal	September 1989
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
The abelian Higgs Kibble model, unitarity of the S-operator Becchi, C.; Rouet, A.; Stora, R. Physics Letters B, Vol. 52, Issue 3 https://doi.org/10.1016/0370-2693(74)90058-6	journal	October 1974
Quantization of Yang-Mills fields in superspace Hirschfeld, Allen C.; Leschke, Hajo Physics Letters B, Vol. 101, Issue 1-2 https://doi.org/10.1016/0370-2693(81)90486-X	journal	April 1981
BRS analysis of Zamolodchikov's spin 2 and 3 current algebra Thierry-Mieg, Jean Physics Letters B, Vol. 197, Issue 3 https://doi.org/10.1016/0370-2693(87)90402-3	journal	October 1987
Some results on local cohomologies in field theory Dubois-Violette, Michel; Henneaux, Marc; Talon, Michel Physics Letters B, Vol. 267, Issue 1 https://doi.org/10.1016/0370-2693(91)90527-W	journal	September 1991
On the gauge-fixed BRST cohomology Henneaux, Marc Physics Letters B, Vol. 367, Issue 1-4 https://doi.org/10.1016/0370-2693(95)01449-7	journal	January 1996
The principle of BRS symmetry: An alternative approach to Yang-Mills theories Baulieu, L.; Thierry-Mieg, J. Nuclear Physics B, Vol. 197, Issue 3 https://doi.org/10.1016/0550-3213(82)90454-0	journal	April 1982
Global aspects of current algebra Witten, Edward Nuclear Physics B, Vol. 223, Issue 2 https://doi.org/10.1016/0550-3213(83)90063-9	journal	August 1983
Covariant quantization of non-Abelian antisymmetric tensor gauge theories Thierry-Mieg, Jean; Baulieu, Laurent Nuclear Physics B, Vol. 228, Issue 2 https://doi.org/10.1016/0550-3213(83)90324-3	journal	November 1983
Chiral anomalies, higher dimensions, and differential geometry Zumino, Bruno; Yong-Shi, Wu; Zee, A. Nuclear Physics B, Vol. 239, Issue 2 https://doi.org/10.1016/0550-3213(84)90259-1	journal	July 1984
Consistent and covariant anomalies in gauge and gravitational theories Bardeen, William A.; Zumino, Bruno Nuclear Physics B, Vol. 244, Issue 2 https://doi.org/10.1016/0550-3213(84)90322-5	journal	October 1984
The topological meaning of non-abelian anomalies Alvarez-Gaumé, L.; Ginsparg, P. Nuclear Physics B, Vol. 243, Issue 3 https://doi.org/10.1016/0550-3213(84)90487-5	journal	September 1984
Cohomology of gauge groups: Cocycles and Schwinger terms Zumino, Bruno Nuclear Physics B, Vol. 253 https://doi.org/10.1016/0550-3213(85)90543-7	journal	January 1985
p-forms and supergravity: Gauge symmetries in curved space Baulieu, L.; Bellon, M. Nuclear Physics B, Vol. 266, Issue 1 https://doi.org/10.1016/0550-3213(86)90178-1	journal	March 1986
Lie algebra cohomology Brandt, Friedemann; Dragon, Norbert; Kreuzer, Maximilian Nuclear Physics B, Vol. 332, Issue 1 https://doi.org/10.1016/0550-3213(90)90038-F	journal	February 1990
The geometry of quantum gauge theories: A superspace formulation of BRST symmetry Hull, C. M.; Spence, B.; Vázquez-Bello, J. L. Nuclear Physics B, Vol. 348, Issue 1 https://doi.org/10.1016/0550-3213(91)90224-L	journal	January 1991
Local BRST cohomology in gauge theories Barnich, Glenn; Brandt, Friedemann; Henneaux, Marc Physics Reports, Vol. 338, Issue 5 https://doi.org/10.1016/S0370-1573(00)00049-1	journal	November 2000
Poisson geometry Weinstein, Alan Differential Geometry and its Applications, Vol. 9, Issue 1-2 https://doi.org/10.1016/S0926-2245(98)00022-9	journal	August 1998
Extended obstruction tensors and renormalized volume coefficients Graham, C. Robin Advances in Mathematics, Vol. 220, Issue 6 https://doi.org/10.1016/j.aim.2008.11.015	journal	April 2009
Connections on Lie algebroids and on derivation-based noncommutative geometry Lazzarini, Serge; Masson, Thierry Journal of Geometry and Physics, Vol. 62, Issue 2 https://doi.org/10.1016/j.geomphys.2011.11.002	journal	February 2012
Formulation of gauge theories on transitive Lie algebroids Fournel, Cédric; Lazzarini, Serge; Masson, Thierry Journal of Geometry and Physics, Vol. 64 https://doi.org/10.1016/j.geomphys.2012.11.005	journal	February 2013
Cartan connections and Atiyah Lie algebroids Attard, J.; François, J.; Lazzarini, S. Journal of Geometry and Physics, Vol. 148 https://doi.org/10.1016/j.geomphys.2019.103541	journal	February 2020
Lie algebroids and the geometry of off-shell BRST Ciambelli, Luca; Leigh, Robert G. Nuclear Physics B, Vol. 972 https://doi.org/10.1016/j.nuclphysb.2021.115553	journal	November 2021
Weyl-ambient geometries Jia, Weizhen; Karydas, Manthos; Leigh, Robert G. Nuclear Physics B, Vol. 991 https://doi.org/10.1016/j.nuclphysb.2023.116224	journal	June 2023
Differential Geometry, Gauge Theories and Gravity Göckeler, M.; Schücker, T.; Nepomechie, Rafael I. Physics Today, Vol. 42, Issue 1 https://doi.org/10.1063/1.2810887	journal	January 1989
Becchi-Rouet-Stora-Tyutin structure for the mixed Weyl-diffeomorphism residual symmetry François, J.; Lazzarini, S.; Masson, T. Journal of Mathematical Physics, Vol. 57, Issue 3 https://doi.org/10.1063/1.4943595	journal	March 2016
Geometrical reinterpretation of Faddeev–Popov ghost particles and BRS transformations Thierry‐Mieg, Jean Journal of Mathematical Physics, Vol. 21, Issue 12 https://doi.org/10.1063/1.524385	journal	December 1980
Geometrical structure of Faddeev–Popov fields and invariance properties of gauge theories Quirós, M.; de Urries, F. J.; Hoyos, J. Journal of Mathematical Physics, Vol. 22, Issue 8 https://doi.org/10.1063/1.525123	journal	August 1981
Superfiber bundle structure of gauge theories with Faddeev–Popov fields Hoyos, J.; Quirós, M.; Mittelbrunn, J. Ramírez Journal of Mathematical Physics, Vol. 23, Issue 8 https://doi.org/10.1063/1.525523	journal	August 1982
Yang–Mills cohomology in four dimensions Bandelloni, Giuseppe Journal of Mathematical Physics, Vol. 27, Issue 10 https://doi.org/10.1063/1.527323	journal	October 1986
A classification of global conformal invariants Boulanger, Nicolas; François, Jordan; Lazzarini, Serge Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 11 https://doi.org/10.1088/1751-8121/ab01af	journal	February 2019
The geometry of $G$-structures Chern, S. S. Bulletin of the American Mathematical Society, Vol. 72, Issue 2 https://doi.org/10.1090/S0002-9904-1966-11473-8	journal	March 1966
Cohomology theory of Lie groups and Lie algebras Chevalley, Claude; Eilenberg, Samuel Transactions of the American Mathematical Society, Vol. 63, Issue 1 https://doi.org/10.1090/S0002-9947-1948-0024908-8	journal	January 1948
Complex analytic connections in fibre bundles Atiyah, M. F. Transactions of the American Mathematical Society, Vol. 85, Issue 1 https://doi.org/10.1090/S0002-9947-1957-0086359-5	journal	January 1957
Axial-Vector Vertex in Spinor Electrodynamics Adler, Stephen L. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2426	journal	January 1969
Conservation of Isotopic Spin and Isotopic Gauge Invariance Yang, C. N.; Mills, R. L. Physical Review, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRev.96.191	journal	October 1954
Gravitational anomalies and thermal Hall effect in topological insulators Stone, Michael Physical Review B, Vol. 85, Issue 18 https://doi.org/10.1103/PhysRevB.85.184503	journal	May 2012
Obstruction tensors in Weyl geometry and holographic Weyl anomaly Jia, Weizhen; Karydas, Manthos Physical Review D, Vol. 104, Issue 12 https://doi.org/10.1103/PhysRevD.104.126031	journal	December 2021
Concept of nonintegrable phase factors and global formulation of gauge fields Wu, Tai Tsun; Yang, Chen Ning Physical Review D, Vol. 12, Issue 12 https://doi.org/10.1103/PhysRevD.12.3845	journal	December 1975
Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar Physical Review D, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevD.88.025040	journal	July 2013
Symmetry Breaking through Bell-Jackiw Anomalies 't Hooft, G. Physical Review Letters, Vol. 37, Issue 1 https://doi.org/10.1103/PhysRevLett.37.8	journal	July 1976
Path-Integral Measure for Gauge-Invariant Fermion Theories Fujikawa, Kazuo Physical Review Letters, Vol. 42, Issue 18 https://doi.org/10.1103/PhysRevLett.42.1195	journal	April 1979
The geometrical setting of gauge theories of the Yang-Mills type Daniel, M.; Viallet, C. M. Reviews of Modern Physics, Vol. 52, Issue 1 https://doi.org/10.1103/RevModPhys.52.175	journal	January 1980
Lie algebroids, gauge theories, and compatible geometrical structures Kotov, Alexei; Strobl, Thomas Reviews in Mathematical Physics, Vol. 31, Issue 04 https://doi.org/10.1142/S0129055X19500156	journal	April 2019
Characteristic Classes of Hermitian Manifolds Chern, Shiing-shen The Annals of Mathematics, Vol. 47, Issue 1 https://doi.org/10.2307/1969037	journal	January 1946
BRST and Superfield Formalism—A Review Bonora, Loriano; Malik, Rudra Prakash Universe, Vol. 7, Issue 8 https://doi.org/10.3390/universe7080280	journal	August 2021
$Q$-Curvature and Poincaré Metrics Fefferman, Charles; Graham, C. Robin Mathematical Research Letters, Vol. 9, Issue 2 https://doi.org/10.4310/MRL.2002.v9.n2.a2	journal	January 2002

Similar Records

Lie algebroids and the geometry of off-shell BRST

Journal Article · 2021 · Nuclear Physics. B · OSTI ID:1821942

Ciambelli, Luca; Leigh, Robert G.

Lie algebroids: spectral sequences and signature

Journal Article · 2003 · Sbornik. Mathematics · OSTI ID:21208341

Kubarski, J; Mishchenko, A S

Lie antialgebras: cohomology and representations

Journal Article · 2008 · AIP Conference Proceedings · OSTI ID:21254872

Ovsienko, V

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Physics

Title: BRST cohomology is Lie algebroid cohomology

Citation Formats

References (59)

Similar Records

Related Subjects