Types of quantum field thories
One way that higher spin gauge theories are thought to naturally arise is as the limiting case of string field theory when the string’s 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 a an infinite collection of massless spinning particles for ever higher spin. Due to their common orgin 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 tension to zero, see at closed string field theory – As an ∞-Chern-Simons theory).
Original articles include
Reviews and lecture notes include
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
G. Bonelli, On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins, Nucl.Phys. B669 (2003) 159-172 (arXiv:hep-th/0305155)
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
M P Blencowe, A consistent interacting massless higher-spin field theory in 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)