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Generally by a higher spin field theory is meant a quantum field theory that involves fields of spin $\gt 2$ (recalling that a spinor field has spin 1/2, a gauge field has spin 1, a gravitino field has spin 3/2 and the field of gravity has spin 2).
Folklore had it that all higher spin field theories with mass-less higher spin fields are inconsistent due to negative norm states (“ghost”) appearing in their quantization. (This argument underlies the dominance of $\mathcal{N} = 1$ 11-dimensional supergravity, see the introduction to the entry 12-dimensional supergravity for more on this).
But then it was discovered that there is a gigher spin gauge theory (Vasiliev 96) which is a kind of higher gauge theory whose field content is an infinite tower of massless fields of ever higher spin.
Ever since the refine folklore says that higher spin theories with a finite number of higher spin field species is inconsistent, but that an infinite tower can fix the problem (…add reference…).
One way that higher spin gauge theories are thought to naturally arise is as the limiting case of string field theory when the string tension is sent to zero (Henneaux-Teitelboim 87, section 2, Gross 88, Sagnotti-Tsulaia 03, Bonelli 03): The excitation spectrum of the string sigma-model contains beyond the massless particles of the effective supergravity theory an infinite tower of massive excitations, of ever higher spin. There are, however, certain limits in which all these masses become negligible to a reference energy scale – the tensionless limit – this is notably so for compactifications on anti de Sitter spaces of small radius. In this limit the string spectrum looks like an infinite collection of massless spinning particles for ever higher spin. Due to their common origin in the string, these share intricate relations among each other, which are argued to be described by higher spin gauge theory. (Notice that at least closed bosonic string field theory is itself already a higher gauge theory, even without sending the string tension to zero, see at closed string field theory – As an ∞-Chern-Simons theory.)
Original articles include
Reviews and lecture notes include the following:
Mikhail Vasiliev, Higher Spin Gauge Theories in Various Dimensions, 27th Johns Hopkins Workshop on Current Problems in Particle Theory: Symmetries and Mysteries of M Theory (arXiv:hep-th/0401177)
Mikhail Vasiliev, Higher spin gauge theories in any dimension talk at String2004 in Moscow (arXiv:hep-th/0409260)
R. Argurio, Glenn Barnich, G. Bonelli, M. Grigoriev (eds.) Higher spin gauge theories Solvay Workshops and Symposia (2004) (pdf)
Xavier Bekaert, S. Cnockaert, Carlo Iazeolla, Mikhail Vasiliev, Nonlinear higher spin theories in various dimensions (arXiv:0503128)
V.E. Didenko, E.D. Skvortsov, Elements of Vasiliev theory (arXiv:1401.2975)
Rakibur Rahman, Massimo Taronna, From Higher Spins to Strings: A Primer (arXiv:1512.07932 )
Pan Kessel, The Very Basics of Higher-Spin Theory (arXiv:1702.03694)
Ivan Vuković, Higher spin theory (arXiv:1809.02179)
Further developments include for instance
The idea that higher spin gauge theory appears as the limiting case of string field theory where the string tension vanishes goes back to
Marc Henneaux, Claudio Teitelboim, section 2 of First And Second Quantized Point Particles Of Any Spin, in Claudio Teitelboim, Jorge Zanelli (eds.) Santiago 1987, Proceedings, Quantum mechanics of fundamental systems 2, pp. 113-152. Plenum Press.
David Gross, High-Energy Symmetries Of String Theory, Phys. Rev. Lett. 60 (1988) 1229.
and is further developed for instance in
Auguste Sagnotti, M. Tsulaia, On higher spins and the tensionless limit of String Theory, Nucl. Phys. B682:83-116, 2004 (arXiv:hep-th/0311257)
G. Bonelli, On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins, Nucl. Phys. B669 (2003) 159-172 (arXiv:hep-th/0305155)
Auguste Sagnotti, M. Taronna, String Lessons for Higher-Spin Interactions, Nucl. Phys. B842:299-361,2011 (arXiv:1006.5242)
Auguste Sagnotti, Notes on Strings and Higher Spins (arXiv:1112.4285)
And conversely:
Rakibur Rahman, Massimo Taronna, From Higher Spins to Strings: A Primer in Stefan Fredenhagen (ed.) Introduction to Higher Spin Theory (arXiv:1512.07932)
Matthias Gaberdiel, Rajesh Gopakumar, String Theory as a Higher Spin Theory, J. High Energ. Phys. (2016) 2016: 85 (arXiv:1512.07237, doi:10.1007/JHEP09(2016)085)
Relation to Kac-Moody algebras is discussed in
Expression in terms of AKSZ sigma-models is discussed in
Chern-Simons theory for higher spin fields is discussed in
Miles Blencowe, A consistent interacting massless higher-spin field theory in $D=2+1$ Classical and quantum gravity, volume 6 no 4 (1998)
E. S. Fradkin, V. Ya. Linetsky, a Superconformal Theory of Massless Higher Spin Fields in D=2+1 (web)
Johan Engquist, Olaf Hohm, Higher-spin Chern-Simons theories in odd dimensions (arXiv:0705.3714)
We list references that discuss the relation of higher spin gauge theory to the AdS/CFT correspondence.
Simone Giombi, Xi Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions (arXiv:0912.3462)
Simone Giombi, Xi Yin, Higher Spins in AdS and Twistorial Holography (arXiv:1004.3736)
Simone Giombi, TASI Lectures on the Higher Spin - CFT duality (arXiv:1607.02967)
Charlotte Sleight, Lectures on Metric-like Methods in Higher Spin Holography (arXiv:1701.08360)
Last revised on September 10, 2018 at 11:03:23. See the history of this page for a list of all contributions to it.