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TMF, 2000, Volume 123, Number 1, Pages 3–25 (Mi tmf1942)  

This article is cited in 19 scientific papers (total in 19 papers)

Cohomology of arbitrary spin currents in $\mathrm{AdS}_3$

M. A. Vasiliev, S. F. Prokushkin

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We study conserved currents of any integer or half-integer spin built from massless scalar and spinor fields in $\mathrm{AdS}_3$. We show that 2-forms dual to the conserved currents in $\mathrm{AdS}_3$ 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 $(T^s,\mathcal D)$ of spin-$s$ currents is defined, and the cohomology group $H^1(T^s,\mathcal D)=\mathbb C^{2s+1}$ is found.


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English version:
Theoretical and Mathematical Physics, 2000, 123:1, 415–435

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Received: 21.06.1999

Citation: M. A. Vasiliev, S. F. Prokushkin, “Cohomology of arbitrary spin currents in $\mathrm{AdS}_3$”, TMF, 123:1 (2000), 3–25; Theoret. and Math. Phys., 123:1 (2000), 415–435

Citation in format AMSBIB
\by M.~A.~Vasiliev, S.~F.~Prokushkin
\paper Cohomology of arbitrary spin currents in $\mathrm{AdS}_3$
\jour TMF
\yr 2000
\vol 123
\issue 1
\pages 3--25
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 1
\pages 415--435

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    This publication is cited in the following articles:
    1. M. A. Vasiliev, O. V. Sheinkman, “Scalar field in an arbitrary dimension from the standpoint of higher-spin gauge theory”, Theoret. and Math. Phys., 123:2 (2000), 683–700  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Fotopoulos A., Irges N., Petkou A.C., Tsulaia M., “Higher spin gauge fields interacting with scalars: the Lagrangian cubic vertex”, Journal of High Energy Physics, 2007, no. 10, 021  crossref  mathscinet  isi  scopus  scopus  scopus
    3. Fotopoulos, A, “GAUGE-INVARIANT LAGRANGIANS FOR FREE AND INTERACTING HIGHER SPIN FIELDS: A REVIEW OF THE BRST FORMULATION”, International Journal of Modern Physics A, 24:1 (2009), 1  crossref  mathscinet  zmath  adsnasa  isi
    4. Bekaert X., Meunier E., “Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions”, Journal of High Energy Physics, 2010, no. 11, 116  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Alkalaev K., “Mixed-Symmetry Tensor Conserved Currents and AdS/CFT Correspondence”, J. Phys. A-Math. Theor., 46:21 (2013), 214007  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    6. Kessel P., Gomez Physics AsGustavo Lucena, Skvortsov E., Taronna M., “Higher spins and matter interacting in dimension three”, J. High Energy Phys., 2015, no. 11, 104  crossref  mathscinet  zmath  isi  elib  scopus
    7. Raeymaekers J., “On matter coupled to the higher spin square”, J. Phys. A-Math. Theor., 49:35 (2016), 355402  crossref  mathscinet  zmath  isi  elib  scopus
    8. Boulanger N., Kessel P., Skvortsov E., Taronna M., “Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal”, J. Phys. A-Math. Theor., 49:9 (2016), 095402  crossref  mathscinet  zmath  isi  elib  scopus
    9. Taronna M., “A note on field redefinitions and higher-spin equations”, J. Phys. A-Math. Theor., 50:7 (2017), 075401  crossref  mathscinet  zmath  isi  scopus
    10. Taronna M., “Pseudo-Local Theories: a Functional Class Proposal”, Higher Spin Gauge Theories, ed. Brink L. Henneaux M. Vasiliev M., World Scientific Publ Co Pte Ltd, 2017, 59–84  crossref  zmath  isi
    11. Taronna M., “On the Non-Local Obstruction to Interacting Higher Spins in Fat Space”, J. High Energy Phys., 2017, no. 5  crossref  mathscinet  isi  scopus  scopus  scopus
    12. Sharapov A., Skvortsov E., “Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality”, Nucl. Phys. B, 921 (2017), 538–584  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Sezgin E. Skvortsov E.D. Zhu Ya., “Chern–Simons Matter Theories and Higher Spin Gravity”, J. High Energy Phys., 2017, no. 7, 133  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. Misuna N.G., “On Current Contribution to Fronsdal Equations”, Phys. Lett. B, 778 (2018), 71–78  crossref  zmath  isi  scopus  scopus  scopus
    15. Kessel P., Mkrtchyan K., “Cubic Interactions of Massless Bosonic Fields in Three Dimensions. II. Parity-Odd and Chern–Simons Vertices”, Phys. Rev. D, 97:10 (2018), 106021  crossref  isi  scopus  scopus  scopus
    16. Mkrtchyan K., “Cubic Interactions of Massless Bosonic Fields in Three Dimensions”, Phys. Rev. Lett., 120:22 (2018), 221601  crossref  isi  scopus  scopus  scopus
    17. Vasiliev M.A., “From Coxeter Higher-Spin Theories to Strings and Tensor Models”, J. High Energy Phys., 2018, no. 8, 051  crossref  isi  scopus
    18. Kuzenko S.M., Ponds M., “Topologically Massive Higher Spin Gauge Theories”, J. High Energy Phys., 2018, no. 10, 160  crossref  mathscinet  zmath  isi  scopus
    19. Sharapov A., Skvortsov E., “Formal Higher Spin Gravities”, Nucl. Phys. B, 941 (2019), 838–860  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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