# Contents

## Idea

Higher spin gauge theory (Vasiliev 96) is a kind of higher gauge theory whose field content is an infinite tower of massless fields of ever higher spin.

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).

## References

### General

Original articles include

Reviews and lecture notes include

• 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 (pdf)

• Mikhail Vasiliev, Higher spin gauge theories in any dimension talk at String2004 in Moscow (pdf)

• R. Argurio, Glenn Barnich, G. Bonelli, M. Grigoriev (eds.) Higher spin gauge theories Solvay Workshops and Symposia (2004) (pdf)

Further developments include for instance

• Johan Engquist, Olaf Hohm, Geometry and dynamics of higher-spin frame fields (arXiv:0708.1391)

### Relation to string theory

The idea that higher spin gauge theory appears as the limiting case of string field theory where the string tension vanishes goes back to

and is further developed for instance in

### Relation to other systems

Relation to Kac-Moody algebras is discussed in

Expression in terms of AKSZ sigma-models is discussed in

• K.B. Alkalaev, Maxim Grigoriev, E.D. Skvortsov, Uniformizing higher-spin equations (arXiv:1409.6507)

### Higher spin Chern-Simons theory

Chern-Simons theory for higher spin fields is discussed in

• M P 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)

### Relation to holography

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)

Revised on August 25, 2015 04:15:06 by Urs Schreiber (147.231.89.193)