On the local frame in nonlinear higher-spin equations

Abstract

Properties of the resolution operator d * loc in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor Y , Z variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution d * loc differs from the conventional De Rham resolution d * Z by a non-local shift.

Current interactions and holography from the 0-form sector of nonlinear higher-spin equations

“…The same time the results of [46] showing that the field redefinition found in this paper is essentially nonlocal are in agreement with the analysis of [53] where it was argued that a field redefinition bringing the nonlocal setup resulting from the standard homotopy analysis of nonlinear equations to any local form is essentially nonlocal. The interpretation of the results of this paper given in [46] provides however a starting point for elaboration a perturbative scheme that operates entirely with local or minimally nonlocal results at higher orders with no reference to nonlocal field redefinitions at all.…”

“…The same time, it elucidates deep geometric structures underlying the perturbative analysis of HS theory, relating homotopy integrals over different types of simplexes. This field redefinition not only determines relative coefficients in front of different current interactions but also suggests a proper criterium of (non)locality in nonlinear AdS 4 HS theory, further elaborated in [46] where it is shown in particular that the results obtained in this paper are unambiguously selected by the proper locality criterion of higher-order corrections. It should be stressed that the analysis of the 0-form sector of this paper is fully informative implying locality in the 1-form sector up to possible gauge artifacts.…”

“…If at most a finite number of coefficients a n,m is nonzero, field redefinition (1.1) is genuinely local. Based on the results of this paper, in [46] we conjecture a restriction on the coefficients analogous to a nm appropriate for the definition of the local frame in the twistor-like formalism of the standard formulation of nonlinear HS equations of motion in AdS 4 [47]. Importance of the proper definition of locality was originally raised in [48] where it was shown that by a field redefinition of the form (1.1) it is possible to get rid of the currents…”

“…In particular in [49] a proposal was put forward on the part of the problem associated with the exponential factors resulting from so-called inner Klein operators while the structure of the preexponential factors was only partially determined. In [46], the results of [49] are extended to the preexponential factors at the quadratic order.…”

“…Note that the analysis of [46] refers mainly to the locality of the final result that should not be confused with the issue of (non)locality of the field redefinition from the originally nonlocal setup to the local one. The same time the results of [46] showing that the field redefinition found in this paper is essentially nonlocal are in agreement with the analysis of [53] where it was argued that a field redefinition bringing the nonlocal setup resulting from the standard homotopy analysis of nonlinear equations to any local form is essentially nonlocal.…”