Abstract
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.
Highlights
Do not have propagating degrees of freedom
Chiral HiSGRA can be interesting for a number of reasons: (i) it has a simple action; (ii) it is shown to be UV-finite at one-loop [15,16,17] and it is expected to be one-loop exact; (iii) it captures a subset of correlation functions of Chern-Simons matter theories [18]; (iv) its one-loop amplitudes in flat space contain all helicity plus one-loop amplitudes of perturbative QCD [17]; (v) Chiral HiSGRA is very close to self-dual Yang-Mills (SDYM) and self-dual Gravity (SDGRA) theories [19], which are of great importance on their own
When expanded over the AdS4-background the actions should agree with the classification of vertices in the lightcone gauge obtained in [85] and with contractions of the cubic terms of Chiral HiSGRA in AdS4 [18]
Summary
The spin one field (gauge field) is usually described by an object with a single spacetime index. The spin two field (graviton) is described by the metric perturbation, which is an object with two spacetime indices. It is not surprising that the standard Fronsdal description of higher spin fields, see below, is based on a generalisation of this and uses objects with many spacetime indices. It has been known for a long time that there exists an alternative description of (free) higher spin fields. We will first review the standard Fronsdal approach, and motivate and develop the alternative description
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