Abstract
We give an introduction to the so-called tensorial, matrix or hyperspace approach to the description of massless higher-spin fields.
Highlights
Every consistent theory of interacting higher spin fields necessarily includes an infinite number of such fields
The invariance under Q–supersymmetry implies that they depend on the superinvariant intervals Zij, i.e., hΦ( X1, θ1 )Φ( X1 )b∆2 ( (X2), θ2 )Φ( X2 )b∆3 ( (X3), θ3 )i = W ( Z12, Z23, Z31 ), (180)
If the value of ∆ were restricted by superconformal symmetry to its canonical value and no anomalous dimensions were allowed one would conclude that the conformal fixed point is that of the free theory
Summary
Every consistent theory of interacting higher spin fields necessarily includes an infinite number of such fields. In the method of tensorial (super)spaces, one considers theories in multi-dimensional space–times, but in this case the extra dimensions are introduced in such a way that they generate the fields with higher spins instead of the fields with increasing masses. We will review main features and latest developments of the tensorial space approach, and associated generalized conformal theories It is mainly based on Papers [3,8,10,13,23,24,27]. We show that the field equations on flat hyperspaces and Sp(n) group manifolds can be transformed into each other by performing a generalized conformal rescaling of the hyperfields. Appendices contain some technical details such as conventions used in the review, a derivation of the field equations on Sp(n) group manifolds and some useful identities
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