Abstract
This is the first paper in a series of three dealing with HS theories in flat spacetime. It is divided in three parts. The first part is an elaboration on the method of effective action, initiated in a previous paper. We study the properties of correlators of currents in the free fermion coupled to external higher spin (HS) potentials, and develop techniques for their explicit calculation. In particular we show how they can be calculated via ordinary Feynman diagram techniques. We also introduce the concept of curvedL_infty algebra and show how it can be realized in the context of the fermion model. In part II we compare the results of the scalar model and those of the fermion model (coupled to HS fields). We show that the HS field formulation coming from the scalar model is the ‘square’ of the one ensuing from the fermion model. Finally, in part III, we analyse the possible obstructions that one may meet in constructing the effective action: these are the analogues of anomalies in ordinary gauge theories. We provide explicit and compact formulas of the latter.
Highlights
(super)string theories, it has been known that infinite towers of higher spin fields can soften the UV behaviour in a drastic way
We show that the higher spin (HS) field formulation coming from the scalar model is the ‘square’ of the one ensuing from the fermion model
Studies of the massless HS theories in flat spacetime clearly suggest that such theories must violate some of the usual QFT assumptions, which are assumed in no-go theorems: either locality, or minimal coupling to gravity, or finiteness of the number of particles with the mass below any finite energy scale
Summary
There are some dissuasive elements in the story. Even if we ignore the experimental evidence against the existence of elementary HS particles, there seem to be theoretical obstructions: there are in the literature several no-go theorems prohibiting, under some rather standard assumptions, the existence of massless HS particles in a flat spacetime. Our idea here is to take the universality of the HS structure as a sign that the HS symmetries obtained by linearly coupling HS fields to matter may be exact This assumption is supported by an observation from [15] that actions for HS fields invariant under HS transformation (10) have an L∞ symmetry, a property shared by many consistent theories. We will abandon small scale cabotage around the idea of effective action and launch ourselves in a new enterprise: instead of trying to derive explicit actions by integrating out (scalar or fermion) matter fields, we will use the wisdom (formulas and constructs) acquired in this and previous papers to integrate L∞, that is to determine classical (perturbatively) local theories which automatically satisfy the L∞ relations and in particular enjoy the HS gauge invariance/covariance. We proceed to some sample calculations of 1- and 2-point correlator and show the connection of the perturbative method outlined in [15] with the more traditional perturbative approach based on Feynman diagrams
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