Abstract
A new class of shifted homotopy operators in higher-spin gauge theory is introduced. A sufficient condition for locality of dynamical equations is formulated and Pfaffian Locality Theorem identifying a subclass of shifted homotopies that decrease the degree of non-locality in higher orders of the perturbative expansion is proven.
Highlights
Nonlinear field equations for 4d massless fields of all spins were found in [1, 2]
In this paper we explain how to extend the class of homotopy operators in HS theory to make it possible to systematically analyze locality of interactions derived from nonlinear HS equations
It is shown that a number of available homotopy operators increases quickly with the order of nonlinearity, containing in particular a subclass of homotopy operators that lead directly to the known lower-order local results as shown explicitly in [18]
Summary
Nonlinear field equations for 4d massless fields of all spins were found in [1, 2]. The most symmetric vacuum solution to these equations describes AdS4. In [5] it was shown that from the perspective of the full nonlinear HS equations the field redefinition found in [3] has distinguished properties indicating that it leads to minimal order of non-locality in the higher orders It was not clear how the homotopy technics should be modified to lead directly to the correct local results in the perturbative analysis of HS equations with no reference to field redefinitions. The main aim of this paper is to generalize the conventional homotopy technics in such a way that it will give immediately correct local results in the lowest order Based on this generalization we prove a theorem showing how to choose the proper class of homotopy operators to decrease the level of non-locality of HS equations in higher orders as well. Unfolded field equations for free massless fields of all spins in the AdS4 are [17]
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