Higher Spin Theory and Holography

Annotation

Models involving higher spin gauge fields arise naturally in different areas of modern high energy physics including string (field) theory, modified gravities and holographic correspondence. In the present course we give a systematic introduction into higher spin theories, which includes: free fields on constant curvature backgrounds and their relation to representation theory, various approaches to interactions of higher spin gauge fields, basic models of non-linear higher spin theories as well as the associated mathematical methods. Part of the course is devoted to holographic duality, which relates higher spin theories in anti de Sitter space to conformal field theories on its boundary.

Course plan

1. Fields as representations of the symmetry groups. Wigner’s classification of unitary irreducible representations of the Poincare group. 
2. Covariant equations of motion and gauge symmetries of fields, carrying unitary irreducible representations of the Poincare group. The light cone gauge and degrees of freedom.
3. Fronsdal fields and their Lagrangian description.
4. Fields in anti-de Sitter space as representations of the isometry group. Covariant description and Fronsdal theory in anti-de Sitter space. 
5. Dirac singletons and the Flato-Fronsdal theorem.
6. Higher spin algebras as higher symmetries of singletons. Higher spin algebras in terms of the star product.
7. Interactions of gauge fields. The Noether procedure. 
8. No-go theorems.
9. Higher spin holography and the Klebanov-Polyakov conjecture.
10. Frame-like formalism. Topological theories in three dimensions, the Blencowe theory.
11. Higher spin theories in the light-cone gauge. Chiral higher spin theories.
12. Conformal higher spin fields. Non-linear conformal higher spin theory.

Literature

1. S. Weinberg, The Quantum Theory of Fields. Cambridge University Press, 1996 
2. X. Bekaert, N. Boulanger, The Unitary representations of the Poincare group in any spacetime dimension (2006), hep-th/0611263
3. X.Bekaert, S.Cnockaert, C.Iazeolla and M.A.Vasiliev, ''Nonlinear higher spin theories in various dimensions,'' In Higher spin gauge theories: Proceedings, 1st Solvay Workshop : Brussels, Belgium, 12-14 May, 2004 R. Argurio (ed.) et all, [hep-th/0503128]
4. S. Giombi, TASI Lectures on the Higher Spin - CFT duality, [arXiv:1607.02967]
5. V.E. Didenko and E.D. Skvortsov,''Elements of Vasiliev theory,'' arXiv:1401.2975 [hep-th].
6. I.R.Klebanov and A.M.Polyakov, ''AdS dual of the critical O(N) vector model,'' Phys. Lett. B 550, 213 (2002) [hep-th/0210114]
7. J. Maldacena, Zhiboedov, A. Constraining conformal field theories with a slightly broken higher spin symmetry. Class.Quant.Grav., 2013, 30, 104003, [arXiv:1204.3882]