Abstract
Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic couplings with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of 1/□ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities in the general quartic Noether procedure solution with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in d = 4, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.
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References
A.K.H. Bengtsson, Notes on cubic and quartic light-front kinematics, arXiv:1604.01974 [INSPIRE].
A.K.H. Bengtsson, Investigations into light-front quartic interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes, JHEP 12 (2016) 134 [arXiv:1607.06659] [INSPIRE].
D. Ponomarev and A.A. Tseytlin, On quantum corrections in higher-spin theory in flat space, JHEP 05 (2016) 184 [arXiv:1603.06273] [INSPIRE].
E. Conde, E. Joung and K. Mkrtchyan, Spinor-helicity three-point amplitudes from local cubic interactions, JHEP 08 (2016) 040 [arXiv:1605.07402] [INSPIRE].
C. Sleight and M. Taronna, Higher-spin algebras, holography and flat space, JHEP 02 (2017) 095 [arXiv:1609.00991] [INSPIRE].
D. Ponomarev and E.D. Skvortsov, Light-front higher-spin theories in flat space, J. Phys. A 50 (2017) 095401 [arXiv:1609.04655] [INSPIRE].
D. Ponomarev, Off-shell spinor-helicity amplitudes from light-cone deformation procedure, JHEP 12 (2016) 117 [arXiv:1611.00361] [INSPIRE].
P. Haehnel and T. McLoughlin, Conformal higher spin theory and twistor space actions, arXiv:1604.08209 [INSPIRE].
T. Adamo, P. Hähnel and T. McLoughlin, Conformal higher spin scattering amplitudes from twistor space, JHEP 04 (2017) 021 [arXiv:1611.06200] [INSPIRE].
R. Roiban and A.A. Tseytlin, On four-point interactions in massless higher spin theory in flat space, JHEP 04 (2017) 139 [arXiv:1701.05773] [INSPIRE].
R.R. Metsaev, Poincaré invariant dynamics of massless higher spins: fourth order analysis on mass shell, Mod. Phys. Lett. A 6 (1991) 359 [INSPIRE].
R.R. Metsaev, S matrix approach to massless higher spins theory. 2: the case of internal symmetry, Mod. Phys. Lett. A 6 (1991) 2411 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic interaction terms for arbitrary spin, Nucl. Phys. B 227 (1983) 31 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and N. Linden, Interacting higher spin gauge fields on the light front, Class. Quant. Grav. 4 (1987) 1333 [INSPIRE].
S. Weinberg, Photons and gravitons in S matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135 (1964) B1049.
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, Rev. Mod. Phys. 84 (2012) 987 [arXiv:1007.0435] [INSPIRE].
R. Rahman and M. Taronna, From higher spins to strings: a primer, arXiv:1512.07932 [INSPIRE].
M. Taronna, Higher-spin interactions: four-point functions and beyond, JHEP 04 (2012) 029 [arXiv:1107.5843] [INSPIRE].
M. Taronna, Higher-Spin Interactions: three-point functions and beyond, Ph.D. thesis, Scuola Normale Superiore, Pisa, Italy (2012), arXiv:1209.5755 [INSPIRE].
A. Sagnotti and M. Taronna, String lessons for higher-spin interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [INSPIRE].
S. Leclercq, Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds, arXiv:1009.4834 [INSPIRE].
X. Bekaert, N. Boulanger and S. Leclercq, Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex, J. Phys. A 43 (2010) 185401 [arXiv:1002.0289] [INSPIRE].
P. Dempster and M. Tsulaia, On the structure of quartic vertices for massless higher spin fields on Minkowski background, Nucl. Phys. B 865 (2012) 353 [arXiv:1203.5597] [INSPIRE].
E. Joung and M. Taronna, Cubic-interaction-induced deformations of higher-spin symmetries, JHEP 03 (2014) 103 [arXiv:1311.0242] [INSPIRE].
G. Barnich and M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 [hep-th/9304057] [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Cohomology of arbitrary spin currents in AdS 3, Theor. Math. Phys. 123 (2000) 415 [hep-th/9907020] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Towards holographic higher-spin interactions: four-point functions and higher-spin exchange, JHEP 03 (2015) 170 [arXiv:1412.0016] [INSPIRE].
M.A. Vasiliev, Star-product functions in higher-spin theory and locality, JHEP 06 (2015) 031 [arXiv:1502.02271] [INSPIRE].
P. Kessel, G. Lucena Gómez, E. Skvortsov and M. Taronna, Higher spins and matter interacting in dimension three, JHEP 11 (2015) 104 [arXiv:1505.05887] [INSPIRE].
N. Boulanger, P. Kessel, E.D. Skvortsov and M. Taronna, Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal, J. Phys. A 49 (2016) 095402 [arXiv:1508.04139] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS interactions in higher-spin gravity from conformal field theory, JHEP 11 (2015) 149 [arXiv:1508.04292] [INSPIRE].
E.D. Skvortsov and M. Taronna, On locality, holography and unfolding, JHEP 11 (2015) 044 [arXiv:1508.04764] [INSPIRE].
M. Taronna, Pseudo-local Theories: A Functional Class Proposal, in the proceedings of the International Workshop on Higher Spin Gauge Theories, November 4-6, Singapore (2015), arXiv:1602.08566 [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Bulk quartic vertices from boundary four-point correlators, in the proceedings of the International Workshop on Higher Spin Gauge Theories, November 4-6, Singapore (2015), arXiv:1602.08570 [INSPIRE].
M. Taronna, A note on field redefinitions and higher-spin equations, EPJ Web Conf. 125 (2016)05025 [arXiv:1607.04718] [INSPIRE].
C. Sleight, Interactions in higher-spin gravity: a holographic perspective, PH.D. thesis, Munich Univerity, Munich, Germany (2015), arXiv:1610.01318 [INSPIRE].
C. Sleight, Lectures on Higher Spin Holography, talk give at the 12th Modave Summer School in Mathematical Physics, September 11-17, Modave, Belgium (2016), arXiv:1701.08360 [INSPIRE].
C. Sleight and M. Taronna, Higher spin interactions from conformal field theory: the complete cubic couplings, Phys. Rev. Lett. 116 (2016) 181602 [arXiv:1603.00022] [INSPIRE].
M. Porrati, Universal limits on massless high-spin particles, Phys. Rev. D 78 (2008) 065016 [arXiv:0804.4672] [INSPIRE].
C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].
F.A. Berends, G.J.H. Burgers and H. van Dam, On the theoretical problems in constructing interactions involving higher spin massless particles, Nucl. Phys. B 260 (1985) 295 [INSPIRE].
F.A. Berends, G.J.H. Burgers and H. Van Dam, On spin three selfinteractions, Z. Phys. C 24 (1984)247 [INSPIRE].
E. Joung, L. Lopez and M. Taronna, Solving the Noether procedure for cubic interactions of higher spins in (A)dS, J. Phys. A 46 (2013) 214020 [arXiv:1207.5520] [INSPIRE].
N. Boulanger, S. Leclercq and P. Sundell, On the uniqueness of minimal coupling in higher-spin gauge theory, JHEP 08 (2008) 056 [arXiv:0805.2764] [INSPIRE].
R. Manvelyan, K. Mkrtchyan and W. Rühl, General trilinear interaction for arbitrary even higher spin gauge fields, Nucl. Phys. B 836 (2010) 204 [arXiv:1003.2877] [INSPIRE].
A. Fotopoulos and M. Tsulaia, On the tensionless limit of string theory, off-shell higher spin interaction vertices and BCFW recursion relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].
E. Joung and M. Taronna, Cubic interactions of massless higher spins in (A)dS: metric-like approach, Nucl. Phys. B 861 (2012) 145 [arXiv:1110.5918] [INSPIRE].
M.A. Vasiliev, Current Interactions, Locality and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations, arXiv:1605.02662 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
R. Rahman and M. Taronna, Comments on higher-spin fields in nontrivial backgrounds, in the proceedings of the International Workshop on Higher Spin Gauge Theories, November 4-6, Singapore (2015), arXiv:1603.03050 [INSPIRE].
J.E. Paton and H.-M. Chan, Generalized veneziano model with isospin, Nucl. Phys. B 10 (1969) 516 [INSPIRE].
J.H. Schwarz, Superstring theory, Phys. Rept. 89 (1982) 223 [INSPIRE].
D. Francia, J. Mourad and A. Sagnotti, Current exchanges and unconstrained higher spins, Nucl. Phys. B 773 (2007) 203 [hep-th/0701163] [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, On higher spin interactions with matter, JHEP 05 (2009) 126 [arXiv:0903.3338] [INSPIRE].
M. Taronna, Higher spins and string interactions, arXiv:1005.3061 [INSPIRE].
N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Inconsistency of interacting, multigraviton theories, Nucl. Phys. B 597 (2001) 127 [hep-th/0007220] [INSPIRE].
R. Roiban and A. Tseytlin, On higher-spin scattering in flat space, (2016).
E. Joung, S. Nakach and A.A. Tseytlin, Scalar scattering via conformal higher spin exchange, JHEP 02 (2016) 125 [arXiv:1512.08896] [INSPIRE].
M. Beccaria, S. Nakach and A.A. Tseytlin, On triviality of S-matrix in conformal higher spin theory, JHEP 09 (2016) 034 [arXiv:1607.06379] [INSPIRE].
M. Henneaux and R. Rahman, Note on gauge invariance and causal propagation, Phys. Rev. D 88 (2013) 064013 [arXiv:1306.5750] [INSPIRE].
A.K.H. Bengtsson, Quartic amplitudes for Minkowski higher spin, in the proceedings of the International Workshop on Higher Spin Gauge Theories, November 4-6, Singapore (2015), arXiv:1605.02608 [INSPIRE].
R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [INSPIRE].
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ArXiv ePrint: 1701.05772
Postdoctoral Researcher of the Fund for Scientific Research-FNRS Belgium (Massimo Taronna).
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Taronna, M. On the non-local obstruction to interacting higher spins in flat space. J. High Energ. Phys. 2017, 26 (2017). https://doi.org/10.1007/JHEP05(2017)026
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DOI: https://doi.org/10.1007/JHEP05(2017)026