Abstract
We formulate the equations of motion of a free scalar field in the flat and AdS spaces of arbitrary dimension in the form of “higher-spin” covariant constancy conditions. The Klein-Gordon equation describes a nontrivial cohomology of a certain “σ_-complex.” The action principle for a scalar field is formulated in terms of the “higher-spin” covariant derivatives for an arbitrary mass in AdSd and for a nonzero mass in the flat space. The free-field part of the constructed action coincides with the standard first-order Klein-Gordon action, but the interaction part is different because of the presence of an infinite set of auxiliary fields, which do not contribute at the free level. We consider the example of Yang-Mills current interaction and show how the proposed action generates the pseudolocally exact form of the matter currents in AdSd.
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References
J. Gervais and M. V. Saveliev, “Progress in classically solving ten-dimensional supersymmetric reduced Yang-Mills theories,” Preprint hep-th/9811108 (1998).
M. A. Vasiliev, “Higher-spin gauge theories: Star-product and AdS space,” Preprint hep-th/9910096 (1999).
M. A. Vasiliev,Int. J. Mod. Phys. D,5, 763 (1976); Preprint hep-th/9611024 (1996).
M. A. Vasiliev,Phys. Lett. B,285, 225 (1992).
E. S. Fradkin and M. A. vasiliev,Phys. Lett. B,189, 89 (1987);Nucl. Phys. B,291, 141 (1987).
M. A. Vasiliev,Ann. Phys.,190, 59 (1989).
S. E. Konstein and M. A. Vasiliev,Nucl. Phys. B,331, 475 (1990).
S. F. Prokushkin and M. A. vasiliev,Phys. Lett. B,464, 53 (1999); Preprint hep-th/9906149 (1999); M. A. Vasiliev and S. F. Prokushkin,Theor. Math. Phys.,123, 415 (2000); Preprint hep-th/9907020 (1999).
S. M. Klishevich,Class. Q. Grav.,16, 2915 (1999); Preprint hep-th/9812005 (1998).
I. L. Buchbinder, D. M. Gitman, V. A. Krykhtin, and V. D. Pershin, “Equations of motion for massive spin-2 field coupled to gravity,” Preprint hep-th/9910188 (1999).
M. A. Vasiliev,Fortschr. Phys.,35, 741 (1987).
M. A. Vasiliev,Class. Q. Grav.,11, 649 (1994).
S. F. Prokushkin and M. A. Vasiliev,Nucl. Phys. B,545, 385 (1999); Preprint hep-th/9806236 (1998).
E. S. Fradkin and M. A. Vasiliev,Ann. Phys.,177, 63 (1987).
V. E. Lopatin and M. A. Vasiliev,Mod. Phys. Lett. A,3, 257 (1988).
A. V. Barabanshchikov, S. F. Prokushkin, and M. A. Vasiliev,Theor. Math. Phys.,110, 295 (1997); Preprint hep-th/9609034 (1996).
J. Maldacena, “The large-N limit of superconformal field theories and supergravity,” Preprint hep-th/9711200 (1997); S. Ferrara and C. Fronsdal, “Conformal Maxwell theory as a singleton field theory onADS 5, IIB branes, and duality,” Preprint hep-th/9712239 (1997); M. Gunaydin and D. Minic, “Singletons, doubletons, andM-theory,” Preprint hep-th/9802047 (1998); S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Preprint hep-th/9802109 (1998); E. Witten, “Anti-de Sitter space and holography,” hep-th/9802150 (1998); O. Aharony, S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, “Large-N field theories, string theory, and gravity,” hep-th/9905111 (1999).
M. Green, J. Schwarz, and E. Witten,Superstring Theory, Vols. 1, 2, Cambridge Univ. Press, New York (1987).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 323–344, May, 2000.
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Vasiliev, M.A., Shaynkman, O.V. Scalar field in an arbitrary dimension from the standpoint of higher-spin Gauge theory. Theor Math Phys 123, 683–700 (2000). https://doi.org/10.1007/BF02551402
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DOI: https://doi.org/10.1007/BF02551402