On BF-type higher-spin actions in two dimensions
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Springer
Received: February 19, Revised: April 28, Accepted: May 7, Published: May 29,
2020 2020 2020 2020
Konstantin Alkalaeva,b,c and Xavier Bekaertd a
I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky ave. 53, 119991 Moscow, Russia b Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Leninskie Gory, GSP-1, 119991 Moscow, Russia c Department of General and Applied Physics, Moscow Institute of Physics and Technology, Institutskiy per. 7, Dolgoprudnyi, 141700 Moscow region, Russia d Institut Denis Poisson, Unit´e Mixte de Recherche 7013, Universit´e de Tours, Universit´e d’Orl´eans, CNRS, Parc de Grandmont, 37200 Tours, France
E-mail: [email protected], [email protected] Abstract: 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. Keywords: Higher Spin Gravity, Higher Spin Symmetry ArXiv ePrint: 2002.02387
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)158
JHEP05(2020)158
On BF-type higher-spin actions in two dimensions
Contents 1
2 Higher-spin symmetries in two dimensions
4
3 Linearized higher-spin equations in two dimensions
6
4 Higher-spin Jackiw-Teitelboim gravity
7
5 Extended higher-spin BF-type theory
9
6 Concluding remarks
1
15
Introduction
The problem of constructing interacting theories of higher-spin (HS) gauge fields is notoriously difficult, especially at the level of the action (see e.g. [1, 2] for introductory reviews). In fact, in dimensions four and higher the examples of fully nonlinear actions compatible with the minimal coupling to the spin-two subsector are pretty scarce although such cubic interaction vertices are known since a long time [3, 4]. On the one hand, for conformal HS gravity there exists a perturbatively local action [5, 6] (see also [7]) in any even dimension, whose low-spin truncation gives Maxwell and Weyl actions. Unfortunately, this action expanded around conformally flat background is higher-derivative and thereby clashes with pertubative unitary. On the other hand, nonlinear equations [8] of four-dimensional HS (super)gravity are known since several decades (and their higher-dimensional bosonic analogue [9] since more than a decade) but it was only recently that action functionals were proposed [10, 11] (see also the review [12]) as an off-shell formulation of minimal bosonic four-dimensional HS gravity. The action principles from [10, 11] share the unusual property of being formulated in terms of diff
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