Unconstrained Lagrangian Formulation for Bosonic Continuous Spin Theory in Flat Spacetime of Arbitrary Dimension (2404.14118v6)
Abstract: We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter $\mu$ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including $\mu$, similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion(EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including $\mu$. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature.
- Eugene P. Wigner “On Unitary Representations of the Inhomogeneous Lorentz Group” In Annals Math. 40, 1939, pp. 149–204 DOI: 10.2307/1968551
- V. Bargmann and Eugene P. Wigner “Group Theoretical Discussion of Relativistic Wave Equations” In Proc. Nat. Acad. Sci. 34, 1948, pp. 211 DOI: 10.1073/pnas.34.5.211
- “The unitary representations of the Poincar\’e group in any spacetime dimension” In SciPost Phys. Lect. Notes 30, 2021, pp. 1 DOI: 10.21468/SciPostPhysLectNotes.30
- “Quantum fields and interactions of massless particles - the continuous spin case” In Annals Phys. 64, 1971, pp. 211–253 DOI: 10.1016/0003-4916(71)90284-3
- “Continuous spin representations of the Poincare and superPoincare groups” In J. Math. Phys. 43, 2002, pp. 6279 DOI: 10.1063/1.1518138
- Christian Fronsdal “Massless Fields with Integer Spin” In Phys. Rev. D 18, 1978, pp. 3624 DOI: 10.1103/PhysRevD.18.3624
- “Massless Fields with Half Integral Spin” In Phys. Rev. D 18, 1978, pp. 3630 DOI: 10.1103/PhysRevD.18.3630
- Christian Fronsdal “Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space. 7.” In Phys. Rev. D 20, 1979, pp. 848–856 DOI: 10.1103/PhysRevD.20.848
- “Massless, Half Integer Spin Fields in De Sitter Space” In Phys. Rev. D 22, 1980, pp. 1361 DOI: 10.1103/PhysRevD.22.1361
- N. Bouatta, G. Compere and A. Sagnotti “An Introduction to free higher-spin fields” In 1st Solvay Workshop on Higher Spin Gauge Theories, 2004, pp. 79–99 arXiv:hep-th/0409068
- “Nonlinear higher spin theories in various dimensions” In 1st Solvay Workshop on Higher Spin Gauge Theories, 2004, pp. 132–197 arXiv:hep-th/0503128
- “Elements of Vasiliev theory”, 2014 arXiv:1401.2975 [hep-th]
- “Continuous-spin particle field theory with helicity correspondence” In Phys. Rev. D 91, 2015, pp. 025023 DOI: 10.1103/PhysRevD.91.025023
- Victor O. Rivelles “Gauge Theory Formulations for Continuous and Higher Spin Fields” In Phys. Rev. D 91.12, 2015, pp. 125035 DOI: 10.1103/PhysRevD.91.125035
- R.R. Metsaev “Continuous spin gauge field in (A)dS space” In Phys. Lett. B 767, 2017, pp. 458–464 DOI: 10.1016/j.physletb.2017.02.027
- R.R. Metsaev “BRST-BV approach to continuous-spin field” In Phys. Lett. B 781, 2018, pp. 568–573 DOI: 10.1016/j.physletb.2018.04.038
- Xavier Bekaert and Evgeny D. Skvortsov “Elementary particles with continuous spin” In Int. J. Mod. Phys. A 32.23n24, 2017, pp. 1730019 DOI: 10.1142/S0217751X17300198
- Yu.M. Zinoviev “Infinite spin fields in d = 3 and beyond” In Universe 3.3, 2017, pp. 63 DOI: 10.3390/universe3030063
- “Infinite (continuous) spin fields in the frame-like formalism” In Nucl. Phys. B 928, 2018, pp. 182–216 DOI: 10.1016/j.nuclphysb.2018.01.016
- X. Bekaert, M. Najafizadeh and M.R. Setare “A gauge field theory of fermionic Continuous-Spin Particles” In Phys. Lett. B 760, 2016, pp. 320–323 DOI: 10.1016/j.physletb.2016.07.005
- R.R. Metsaev “Fermionic continuous spin gauge field in (A)dS space” In Phys. Lett. B 773, 2017, pp. 135–141 DOI: 10.1016/j.physletb.2017.08.020
- R.R. Metsaev “Continuous-spin mixed-symmetry fields in AdS(5)” In J. Phys. A 51.21, 2018, pp. 215401 DOI: 10.1088/1751-8121/aabcda
- Mojtaba Najafizadeh “Modified Wigner equations and continuous spin gauge field” In Phys. Rev. D 97.6, 2018, pp. 065009 DOI: 10.1103/PhysRevD.97.065009
- Konstantin B. Alkalaev and Maxim A. Grigoriev “Continuous spin fields of mixed-symmetry type” In JHEP 03, 2018, pp. 030 DOI: 10.1007/JHEP03(2018)030
- Konstantin Alkalaev, Alexander Chekmenev and Maxim Grigoriev “Unified formulation for helicity and continuous spin fermionic fields” In JHEP 11, 2018, pp. 050 DOI: 10.1007/JHEP11(2018)050
- Č. Burdík, V.K. Pandey and A. Reshetnyak “BRST–BFV and BRST–BV descriptions for bosonic fields with continuous spin on R1,d−1superscript𝑅1𝑑1R^{1,d-1}italic_R start_POSTSUPERSCRIPT 1 , italic_d - 1 end_POSTSUPERSCRIPT” In Int. J. Mod. Phys. A 35.26, 2020, pp. 2050154 DOI: 10.1142/S0217751X20501547
- Arkady Yu. Segal “A Generating formulation for free higher spin massless fields”, 2001 arXiv:hep-th/0103028
- Mojtaba Najafizadeh “Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes” In Phys. Rev. D 98.12, 2018, pp. 125012 DOI: 10.1103/PhysRevD.98.125012
- “Free geometric equations for higher spins” In Phys. Lett. B 543, 2002, pp. 303–310 DOI: 10.1016/S0370-2693(02)02449-8
- “On the geometry of higher spin gauge fields” In Class. Quant. Grav. 20, 2003, pp. S473–S486 DOI: 10.1088/0264-9381/20/12/313
- “Minimal local Lagrangians for higher-spin geometry” In Phys. Lett. B 624, 2005, pp. 93–104 DOI: 10.1016/j.physletb.2005.08.002
- I.L. Buchbinder, A.V. Galajinsky and V.A. Krykhtin “Quartet unconstrained formulation for massless higher spin fields” In Nucl. Phys. B 779, 2007, pp. 155–177 DOI: 10.1016/j.nuclphysb.2007.03.032
- “Quartet unconstrained formulation for massive higher spin fields” In JHEP 11, 2008, pp. 081 DOI: 10.1088/1126-6708/2008/11/081
- “Description of the higher massless irreducible integer spins in the BRST approach” In Mod. Phys. Lett. A 13, 1998, pp. 1853–1864 DOI: 10.1142/S0217732398001947
- Cestmir Burdik, A. Pashnev and M. Tsulaia “On the Mixed symmetry irreducible representations of the Poincare group in the BRST approach” In Mod. Phys. Lett. A 16, 2001, pp. 731–746 DOI: 10.1142/S0217732301003826
- I.L. Buchbinder, A. Pashnev and M. Tsulaia “Lagrangian formulation of the massless higher integer spin fields in the AdS background” In Phys. Lett. B 523, 2001, pp. 338–346 DOI: 10.1016/S0370-2693(01)01268-0
- I.L. Buchbinder, A. Pashnev and M. Tsulaia “Massless higher spin fields in the AdS background and BRST constructions for nonlinear algebras” In 4th International Workshop on Supersymmetry and Quantum Symmetries: 16th Max Born Symposium, 2002, pp. 3–10 arXiv:hep-th/0206026
- “On higher spin theory: Strings, BRST, dimensional reductions” In Class. Quant. Grav. 21, 2004, pp. S1457–1464 DOI: 10.1088/0264-9381/21/10/018
- I.L. Buchbinder, V.A. Krykhtin and A. Pashnev “BRST approach to Lagrangian construction for fermionic massless higher spin fields” In Nucl. Phys. B 711, 2005, pp. 367–391 DOI: 10.1016/j.nuclphysb.2005.01.017
- “Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions” In Nucl. Phys. B 727, 2005, pp. 537–563 DOI: 10.1016/j.nuclphysb.2005.07.035
- “Gauge invariant Lagrangian construction for massive higher spin fermionic fields” In Phys. Lett. B 641, 2006, pp. 386–392 DOI: 10.1016/j.physletb.2006.08.060
- “Higher-spin geometry and string theory” In J. Phys. Conf. Ser. 33, 2006, pp. 57 DOI: 10.1088/1742-6596/33/1/006
- “On higher spins and the tensionless limit of string theory” In Nucl. Phys. B 682, 2004, pp. 83–116 DOI: 10.1016/j.nuclphysb.2004.01.024
- Mojtaba Najafizadeh “Off-shell supersymmetric continuous spin gauge theory” In JHEP 02, 2022, pp. 038 DOI: 10.1007/JHEP02(2022)038
- Anders K.H. Bengtsson “BRST Theory for Continuous Spin” In JHEP 10, 2013, pp. 108 DOI: 10.1007/JHEP10(2013)108
- I.L. Buchbinder, V.A. Krykhtin and H. Takata “BRST approach to Lagrangian construction for bosonic continuous spin field” In Phys. Lett. B 785, 2018, pp. 315–319 DOI: 10.1016/j.physletb.2018.07.070
- “Towards Lagrangian construction for infinite half-integer spin field” In Nucl. Phys. B 958, 2020, pp. 115114 DOI: 10.1016/j.nuclphysb.2020.115114
- “On the off-shell superfield Lagrangian formulation of 4D, N=1 supersymmetric infinite spin theory” In Phys. Lett. B 829, 2022, pp. 137139 DOI: 10.1016/j.physletb.2022.137139
- “Lagrangian formulation for free 6D6𝐷6D6 italic_D infinite spin field” In Nucl. Phys. B 996, 2023, pp. 116365 DOI: 10.1016/j.nuclphysb.2023.116365
- “BRST construction for infinite spin field on AdS4𝐴𝑑subscript𝑆4AdS_{4}italic_A italic_d italic_S start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT”, 2024 arXiv:2403.14446 [hep-th]
- “Infinite (continuous) spin particle in constant curvature space”, 2024 arXiv:2402.13879 [hep-th]
- “Ideas and methods of supersymmetry and supergravity: Or a walk through superspace”, 1998
- E.P. Wigner “Relativistische Wellengleichungen” In Zeitschrift für Physik 124.7, 1948, pp. 665–684 DOI: 10.1007/BF01668901
- R.R. Metsaev “Shadows, currents and AdS” In Phys. Rev. D 78, 2008, pp. 106010 DOI: 10.1103/PhysRevD.78.106010
- “The Continuous spin limit of higher spin field equations” In JHEP 01, 2006, pp. 115 DOI: 10.1088/1126-6708/2006/01/115
- I.L. Buchbinder, V.A. Krykhtin and P.M. Lavrov “Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space” In Nucl. Phys. B 762, 2007, pp. 344–376 DOI: 10.1016/j.nuclphysb.2006.11.021
- “Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation” In Int. J. Mod. Phys. A 24, 2009, pp. 1–60 DOI: 10.1142/S0217751X09043134
- G.K. Savvidy “Tensionless strings: Physical Fock space and higher spin fields” In Int. J. Mod. Phys. A 19, 2004, pp. 3171–3194 DOI: 10.1142/S0217751X04018312
- J. Mourad “Continuous spin and tensionless strings”, 2004 arXiv:hep-th/0410009
- J. Mourad “Continuous spin particles from a string theory”, 2005 arXiv:hep-th/0504118
- Dario Francia, J. Mourad and A. Sagnotti “Current Exchanges and Unconstrained Higher Spins” In Nucl. Phys. B 773, 2007, pp. 203–237 DOI: 10.1016/j.nuclphysb.2007.03.021
- R.R. Metsaev “Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields” In JHEP 11, 2017, pp. 197 DOI: 10.1007/JHEP11(2017)197
- Xavier Bekaert, Jihad Mourad and Mojtaba Najafizadeh “Continuous-spin field propagator and interaction with matter” In JHEP 11, 2017, pp. 113 DOI: 10.1007/JHEP11(2017)113
- Xavier Bekaert, Euihun Joung and Jihad Mourad “On higher spin interactions with matter” In JHEP 05, 2009, pp. 126 DOI: 10.1088/1126-6708/2009/05/126
- R.R. Metsaev “BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields” In Phys. Lett. B 720, 2013, pp. 237–243 DOI: 10.1016/j.physletb.2013.02.009