Higher Spin Theory - Part I

Abstract

These notes comprise a part of the introductory lectures on Higher Spin Theory presented in the Eighth Modave Summer School in Mathematical Physics. We construct free higher-spin theories and turn on interactions to find that inconsistencies show up in general. Interacting massless fields in flat space are in tension with gauge invariance and this leads to various no-go theorems. While massive fields exhibit superluminal propagation, appropriate non-minimal terms may cure such pathologies as they do in String Theory--a fact that we demonstrate. Given that any interacting massive higher-spin particle is described by an effective field theory, we compute a model independent upper bound on the ultraviolet cutoff in the case of electromagnetic coupling in flat space and discuss its implications. Finally, we consider various possibilities of evading the no-go theorems for massless fields, among which Vasiliev's higher-spin gauge theory is one. We employ the BRST-antifield method for a simple but non-trivial gauge system in flat space to find a non-abelian cubic coupling and to explore its higher-order consistency.

33 pages, references added, to appear in Proceedings of Science

References in corpus (8)

• The Higher Spin/Vector Model Duality
• Universal Limits on Massless High-Spin Particles
• Consistent couplings between spin-2 and spin-3 massless fields
• FV-type action for AdS(5) mixed-symmetry fields
• Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling
• Causal Propagation of a Charged Spin 3/2 Field in an External Electromagnetic Background
• A Model Independent Ultraviolet Cutoff for Theories with Charged Massive Higher Spin Fields
• Intrinsic Cutoff and Acausality for Massive Spin 2 Fields Coupled to Electromagnetism

Cited by in corpus (8)

• BMS Particles in Three Dimensions
• Massive Higher Spins: Effective Theory and Consistency
• From Higher Spins to Strings: A Primer
• Rotating Higher Spin Partition Functions and Extended BMS Symmetries
• Antisymmetric tensor field and spontaneous magnetization in holographic duality
• Aspects of Higher-Spin Theory with Fermions
• Asymmetrically twisted strings
• Second order differential equations for bosons with spin j > 1 and in the bases of general tensor-spinors of rank-2j