{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:58Z","timestamp":1760150938350,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider the superspace BRST and BV description of 4D,N=1 super-Maxwell theory and its non-abelian generalization Super Yang\u2013Mills. By fermionizing the superspace gauge transformation of the gauge superfields, we define the nilpotent superspace BRST symmetry transformation (\ud835\udcc8). After introducing an appropriate set of anti-superfields and defining the superspace antibracket, we use it to construct the BV-BRST nilpotent differential operator (s) in terms of superspace covariant derivatives. The anti-superfield independent terms of s provide a superspace generalization of the Koszul\u2013Tate resolution (\u03b4). In the linearized limit, the set of superspace differential operators that appear in s satisfy a nonlinear algebra which can be used to construct a BRST charge Q, without requiring pure spinor variables. Q acts on the Hilbert space of superfield states, and its cohomology generates the expected superspace equations of motion.<\/jats:p>","DOI":"10.3390\/sym14020256","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T01:43:27Z","timestamp":1643420607000},"page":"256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Superspace BRST\/BV Operators of Superfield Gauge Theories"],"prefix":"10.3390","volume":"14","author":[{"given":"Ioseph Lvovich","family":"Buchbinder","sequence":"first","affiliation":[{"name":"Center of Theoretical Physics, Tomsk State Pedagogical University, 5, 634041 Tomsk, Russia"},{"name":"Laboratory for Theoretical Cosmology, International Center for Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"Jr.","given":"Sylvester James","family":"Gates","sequence":"additional","affiliation":[{"name":"Brown Theoretical Physics Center, 340 Brook Street, Barus Hall, P.O. Box S, Providence, RI 02912, USA"},{"name":"Department of Physics, Brown University, 182 Hope Street, Barus & Holley 545, P.O. Box 1843, Providence, RI 02912, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Koutrolikos","sequence":"additional","affiliation":[{"name":"Brown Theoretical Physics Center, 340 Brook Street, Barus Hall, P.O. Box S, Providence, RI 02912, USA"},{"name":"Department of Physics, Brown University, 182 Hope Street, Barus & Holley 545, P.O. Box 1843, Providence, RI 02912, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/0370-2693(74)90058-6","article-title":"The Abelian Higgs-Kibble Model. Unitarity of the S Operator","volume":"52","author":"Becchi","year":"1974","journal-title":"Phys. Lett. B"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF01614158","article-title":"Renormalization of the Abelian Higgs-Kibble Model","volume":"42","author":"Becchi","year":"1975","journal-title":"Commun. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0003-4916(76)90156-1","article-title":"Renormalization of Gauge Theories","volume":"98","author":"Becchi","year":"1976","journal-title":"Annals Phys."},{"key":"ref_4","unstructured":"Tyutin, I.V. (2008). Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0370-2693(81)90205-7","article-title":"Gauge Algebra and Quantization","volume":"102","author":"Batalin","year":"1981","journal-title":"Phys. Lett. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1103\/PhysRevD.28.2567","article-title":"Quantization of Gauge Theories with Linearly Dependent Generators","volume":"28","author":"Batalin","year":"1983","journal-title":"Phys. Rev. D"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1063\/1.526780","article-title":"Existence Theorem for Gauge Algebra","volume":"26","author":"Batalin","year":"1985","journal-title":"J. Math. Phys."},{"key":"ref_8","first-page":"498","article-title":"Canonical Transformations and the Gauge Dependence in General Gauge Theories. (IN RUSSIAN)","volume":"36","author":"Voronov","year":"1982","journal-title":"Yad. Fiz."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/BF01016448","article-title":"Formulation of Gauge Theories of General Form. I","volume":"50","author":"Voronov","year":"1982","journal-title":"Theor. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1007\/BF01027781","article-title":"Formulation of Gauge Theories of General Form. II. Gauge Invariant Renormalizability and Renormalization Structure","volume":"52","author":"Voronov","year":"1982","journal-title":"Theor. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Buchbinder, I.L., Gates, S.J., and Koutrolikos, K. (2021). Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity. arXiv.","DOI":"10.1007\/JHEP09(2021)077"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0550-3213(86)90155-0","article-title":"Noncommutative Geometry and String Field Theory","volume":"268","author":"Witten","year":"1986","journal-title":"Nucl. Phys. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/0370-2693(87)91391-8","article-title":"String Field Theory in the Siegel Gauge","volume":"188","author":"Bochicchio","year":"1987","journal-title":"Phys. Lett. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0550-3213(87)90096-4","article-title":"Perturbation Theory for Quantized String Fields","volume":"287","author":"Thorn","year":"1987","journal-title":"Nucl. Phys. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0370-1573(89)90015-X","article-title":"String Field Theory","volume":"175","author":"Thorn","year":"1989","journal-title":"Phys. Rept."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0550-3213(93)90388-6","article-title":"Closed string field theory: Quantum action and the B-V master equation","volume":"390","author":"Zwiebach","year":"1993","journal-title":"Nucl. Phys. B"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Taylor, W., and Zwiebach, B. (2003). D-branes, tachyons, and string field theory. Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001): Strings, Branes and Extra Dimensions, World Scientific.","DOI":"10.1142\/9789812702821_0012"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Siegel, W. (1988). Introduction to string field theory. arXiv.","DOI":"10.1142\/0715"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"S1457","DOI":"10.1088\/0264-9381\/21\/10\/018","article-title":"On higher spin theory: Strings, BRST, dimensional reductions","volume":"21","author":"Bekaert","year":"2004","journal-title":"Class. Quant. Grav."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.nuclphysb.2005.01.017","article-title":"BRST approach to Lagrangian construction for fermionic massless higher spin fields","volume":"711","author":"Buchbinder","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/j.nuclphysb.2005.07.035","article-title":"Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions","volume":"727","author":"Buchbinder","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105018","DOI":"10.1103\/PhysRevD.74.105018","article-title":"Constructing the cubic interaction vertex of higher spin gauge fields","volume":"74","author":"Buchbinder","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1002\/prop.200510274","article-title":"On killing tensors and cubic vertices in higher-spin gauge theories","volume":"54","author":"Bekaert","year":"2006","journal-title":"Fortsch. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.nuclphysb.2007.06.006","article-title":"BRST approach to Lagrangian construction for fermionic higher spin fields in (A)dS space","volume":"787","author":"Buchbinder","year":"2007","journal-title":"Nucl. Phys. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"066005","DOI":"10.1103\/PhysRevD.82.066005","article-title":"Interactions of Massless Higher Spin Fields From String Theory","volume":"82","author":"Polyakov","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"093","DOI":"10.1007\/JHEP08(2012)093","article-title":"Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling","volume":"8","author":"Henneaux","year":"2012","journal-title":"J. High Energy Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.physletb.2013.02.009","article-title":"BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields","volume":"720","author":"Metsaev","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/JHEP01(2014)087","article-title":"Gravitational Interactions of Higher-Spin Fermions","volume":"1","author":"Henneaux","year":"2014","journal-title":"J. High Energy Phys."},{"key":"ref_29","first-page":"106","article-title":"BRST Analysis of the Supersymmetric Higher Spin Field Models","volume":"12","author":"Buchbinder","year":"2015","journal-title":"J. High Energy Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.physletb.2018.07.070","article-title":"BRST approach to Lagrangian construction for bosonic continuous spin field","volume":"785","author":"Buchbinder","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"115427","DOI":"10.1016\/j.nuclphysb.2021.115427","article-title":"Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions","volume":"967","author":"Buchbinder","year":"2021","journal-title":"Nucl. Phys. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/JHEP06(2021)097","article-title":"On a gauge-invariant deformation of a classical gauge-invariant theory","volume":"6","author":"Buchbinder","year":"2021","journal-title":"J. High Energy Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1140\/epjc\/s10052-021-09671-y","article-title":"On classical and quantum deformations of gauge theories","volume":"81","author":"Buchbinder","year":"2021","journal-title":"Eur. Phys. J. C"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"136470","DOI":"10.1016\/j.physletb.2021.136470","article-title":"General cubic interacting vertex for massless integer higher spin fields","volume":"820","author":"Buchbinder","year":"2021","journal-title":"Phys. Lett. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1088\/1126-6708\/2000\/04\/018","article-title":"Super Poincare covariant quantization of the superstring","volume":"4","author":"Berkovits","year":"2000","journal-title":"J. High Energy Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1088\/1126-6708\/2002\/02\/009","article-title":"Spinorial cohomology and maximally supersymmetric theories","volume":"2","author":"Cederwall","year":"2002","journal-title":"J. High Energy Phys."},{"key":"ref_37","first-page":"57","article-title":"ICTP lectures on covariant quantization of the superstring","volume":"13","author":"Berkovits","year":"2003","journal-title":"ICTP Lect. Notes Ser."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1088\/1126-6708\/2005\/10\/089","article-title":"Pure spinor formalism as an N=2 topological string","volume":"10","author":"Berkovits","year":"2005","journal-title":"J. High Energy Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3201","DOI":"10.1142\/S0217732310034407","article-title":"D=11 supergravity with manifest supersymmetry","volume":"25","author":"Cederwall","year":"2010","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/978-3-319-03774-5_4","article-title":"Pure spinor superfields\u2014An overview","volume":"153","author":"Cederwall","year":"2014","journal-title":"Springer Proc. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/0370-2693(89)91007-1","article-title":"Lorentz Covariant Quantization of the Heterotic Superstring","volume":"225","author":"Gates","year":"1989","journal-title":"Phys. Lett. B"},{"key":"ref_42","first-page":"244","article-title":"Unconstrained BRST: A New prototype for covariant string field theory?","volume":"9003122","author":"Gates","year":"1990","journal-title":"Conf. Proc. C"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Henneaux, M., and Teitelboim, C. (1992). Quantization of Gauge Systems, Princeton University Press.","DOI":"10.1515\/9780691213866"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0370-2693(78)90135-1","article-title":"Quantization of Relativistic Systems with Boson and Fermion First and Second Class Constraints","volume":"72","author":"Fradkin","year":"1978","journal-title":"Phys. Lett. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/0370-2693(75)90448-7","article-title":"Quantization of Relativistic Systems with Constraints","volume":"55","author":"Fradkin","year":"1975","journal-title":"Phys. Lett. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0370-2693(77)90553-6","article-title":"Relativistic S Matrix of Dynamical Systems with Boson and Fermion Constraints","volume":"69","author":"Batalin","year":"1977","journal-title":"Phys. Lett. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0370-2693(83)90784-0","article-title":"A Generalized Canonical Formalism and Quantization of Reducible Gauge Theories","volume":"122","author":"Batalin","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0370-1573(85)90103-6","article-title":"Hamiltonian Form of the Path Integral for Theories with a Gauge Freedom","volume":"126","author":"Henneaux","year":"1985","journal-title":"Phys. Rept."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01218470","article-title":"Quantum BRST Charge for Quadratically Nonlinear Lie Algebras","volume":"124","author":"Schoutens","year":"1989","journal-title":"Commun. Math. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"082306","DOI":"10.1063\/1.2767537","article-title":"Classical BRST charge for nonlinear algebras","volume":"48","author":"Buchbinder","year":"2007","journal-title":"J. Math. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0920-5632(90)90647-D","article-title":"Lectures on the Antifield-BRST Formalism for Gauge Theories","volume":"18","author":"Henneaux","year":"1990","journal-title":"Nucl. Phys. B Proc. Suppl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/256\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:09:55Z","timestamp":1760134195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,28]]},"references-count":51,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020256"],"URL":"https:\/\/doi.org\/10.3390\/sym14020256","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,1,28]]}}}