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Register a new userOn BF-type higher-spin actions in two dimensions
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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 $hs[lambda]$. The corresponding action functional is of BF-type and generalizes the known topological higher-spin Jackiw-Teitelboim gravity.
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We study $(2,2)$ and $(4,4)$ supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum, the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D $(4,4)$ example is the dimensional reduction of a 4D $N=2$ model, and gives a new way for the spontaneous breaking of extended supersymmetry.
Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature.
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