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Cohomology of arbitrary spin currents in AdS3
Authors:M A Vasiliev  S F Prokushkin
Institution:(1) Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia;(2) Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia
Abstract:We study conserved currents of any integer or half-integer spin built from massless scalar and spinor fields inAdS 3. We show that 2-forms dual to the conserved currents inAdS 3 are exact in the class of infinite expansions in higher derivatives of the matter fields with the coefficients containing inverse powers of the cosmological constant. This property has no analogue in the flat space and may be related to the holography of the AdS spaces. “Improvements” to the physical currents are described as the trivial local current cohomology class. A complex (TS, D) of spin-s currents is defined, and the cohomology group H1(TS, D)= ℂ2s+1is found. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 3–25, April, 2000.
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