We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together with their dilaton-like partners. The spectrum includes local degrees of freedom although the field equations take the form of flatness and covariant constancy conditions because fields take values in a suitable extension of the infinite-dimensional higher-spin algebra 𝔥𝔰[λ]. The corresponding action functional is of BF-type and generalizes the known topological higher-spin Jackiw-Teitelboim gravity.
E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Cubic interaction in extended theories of massless higher spin fields, Nucl. Phys. B 291 (1987) 141 [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, Effective action in a higher-spin background, JHEP 02 (2011) 048 [arXiv:1012.2103] [INSPIRE].
M.A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 285 (1992) 225 [INSPIRE].
C. Arias et al., Action principles for higher and fractional spin gravities, in Proceedings, International Workshop on Higher Spin Gauge Theories, Singapore, 4–6 November 2015, World Scientific, Singapore (2017), pg. 213 [arXiv:1603.04454] [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
J.H. Horne and E. Witten, Conformal gravity in three-dimensions as a gauge theory, Phys. Rev. Lett. 62 (1989) 501 [INSPIRE].
M.P. Blencowe, A consistent interacting massless higher spin field theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].
E.S. Fradkin and V. Ya. Linetsky, Conformal superalgebras of higher spins, Annals Phys. 198 (1990) 252 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
T. Fukuyama and K. Kamimura, Gauge theory of two-dimensional gravity, Phys. Lett. B 160 (1985) 259 [INSPIRE].
E.S. Fradkin and V. Ya. Linetsky, Higher spin symmetry in one-dimension and two-dimensions. 1, Mod. Phys. Lett. A 4 (1989) 2635 [INSPIRE].
E.S. Fradkin and V. Ya. Linetsky, Higher spin symmetry in one-dimension and two-dimensions. 2, Mod. Phys. Lett. A 4 (1989) 2649 [INSPIRE].
B.L. Feigin, Lie algebras gl(λ) and cohomologies of Lie algebras of differential operators, Russ. Math. Surv. 43 (1988) 169.
M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, in Higher spin gauge theories: proceedings, 1st Solvay Workshop, Brussels, Belgium, 12–14 May 2004, pg. 132 [hep-th/0503128] [INSPIRE].
V.E. Lopatin and M.A. Vasiliev, Free massless bosonic fields of arbitrary spin in d-dimensional de Sitter space, Mod. Phys. Lett. A 3 (1988) 257 [INSPIRE].
M. Hazewinkel, N. Gubareni and V.V. Kirichenko, Algebras, rings, and modules: Lie algebras and Hopf algebras, American Mathematical Society, Providence, RI, U.S.A. (2010).
M.A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortsch. Phys. 36 (1988) 33 [INSPIRE].
A.V. Barabanshchikov, S.F. Prokushkin and M.A. Vasiliev, Free equations for massive matter fields in (2 + 1)-dimensional anti-de Sitter space from deformed oscillator algebra, Theor. Math. Phys. 110 (1997) 295 [Teor. Mat. Fiz. 110N3 (1997) 372] [hep-th/9609034] [INSPIRE].
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ArXiv ePrint: 2002.02387
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Alkalaev, K., Bekaert, X. On BF-type higher-spin actions in two dimensions. J. High Energ. Phys. 2020, 158 (2020). https://doi.org/10.1007/JHEP05(2020)158
- Higher Spin Gravity
- Higher Spin Symmetry