Unfolded equations for current interactions of 4 d massless fields as a free system in mixed dimensions
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nfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions1 O. A. Gelfonda,* and M. A. Vasilievb, c,** a
b
Institute of System Research, Russian Academy of Sciences, Moscow, 117218 Russia I. E. Tamm Department of Theoretical Physics, Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia c Theory Group, Physics Department, CERN CH1211, Geneva 23, Switzerland *email: [email protected] **email: [email protected] Received October 30, 2014
Abstract—Interactions of massless fields of all spins in four dimensions with currents of any spin are shown to result from a solution of the linear problem that describes a gluing between a rankone (massless) system and a ranktwo (current) system in the unfolded dynamics approach. Since the ranktwo system is dual to a free rankone higherdimensional system that effectively describes conformal fields in six space–time dimen sions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. An interpretation of the obtained results in the spirit of the AdS/CFT correspon dence is discussed. Contribution for the JETP special issue in honor of V.A.Rubakov’s 60th birthday DOI: 10.1134/S106377611503005X 1
1. INTRODUCTION
Valery Rubakov has a remarkably broad area of sci entific interests, ranging from the theory of funda mental interactions to cosmology. To the volume in honor of Valery’s 60th birthday, we contribute a paper that gives hints on a possible unification of such seem ingly different concepts of quantum field theory (QFT) as conserved currents in lower dimension and free fields in higher dimension. Although such an identification now sounds natural in the context of the AdS/CFT correspondence [1–3], the particular real ization suggested in this paper goes beyond the stan dard setup that allows interpreting current interactions of 4d fields of all spins, including the usual fields of spins 0 ≤ s ≤ 2, in terms of a linear system mixing free conformal fields in four and six dimensions. In fact, part of this work has been presented some time ago at a seminar headed by Rubakov, after which we had a stimulating discussion with Valery on whether it is pos sible to make fields in space–times of different dimen sions directly interact in relativistic field theory. Since then, we have obtained more evidence, including that presented in this paper, that this is not only possible but also can eventually drive us to a better understand ing of fundamental concepts of QFT, including the very concept of space–time. Hence, we believe that 1 The article is published in the original.
this paper is appropriate for the volume in honor of Valery Rubakov. Specifically, we consider field equations for mass less fields of all spins in a fourdimensional antide Sitter space in the lowest order in interactions accounting for the contribution of conserved currents built from bilinears of the same set of massless fields. The problem is analyzed in the framework
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