Interactions of chiral two-forms

Two issues regarding the interactions of the chiral two-forms are reviewed. First, the problem of constructing Lorentz-invariant self-couplings of a single chiral two-form is investigated in the light of the Dirac-Schwinger condition on the energy-momentum tensor commutation relations. We show how the Perry-Schwarz condition follows from the Dirac-Schwinger criterion and point out that consistency of the gravitational coupling is automatic. Secondly, we study the possible local deformations of chiral two-forms. This problem reduces to the study of the local BRST cohomological group at ghost number zero. We proof that the only consistent deformations of a system of free chiral two-forms are (up to redefinitions) deformations that do not modify the abelian gauge symmetries of the free theory. The consequence of this result for a system consisting of a number of parallel M5-branes is explained.Comment: 6 pages. References added. Modified presentation. Talk given at the TMR-meeting `Quantum aspects of gauge theories, supersymmetry and unification', ENS (Paris), September 1-7, 1999 and at the `9th Midwest Geometry Conference', Univ. of Missouri (Columbia), November 5-7, 1999. From joint work with M. Henneaux and A. Sevri

Singletons and their maximal symmetry algebras

Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping algebra of the conformal algebra on these modules. These objects appear in a wide variety of areas of theoretical physics: AdS/CFT correspondence, electric-magnetic duality, higher-spin multiplets, infinite-component Majorana equations, higher-derivative symmetries, etc. Singletons and higher-spin algebras are reviewed through a list of their many equivalent definitions in order to approach them from various perspectives. The focus of this introduction is on the symmetries of a singleton: its maximal algebra and the manifest realization thereof.Comment: 34 pages, published (splitted into two distinct pieces) in the proceedings of the "7th spring school and workshop on quantum field theory & Hamiltonian systems" and of the "6th mathematical physics meeting: summer school and conference on modern mathematical physics", v2: references (and related comments) adde

Gauge invariants and Killing tensors in higher-spin gauge theories

In free completely symmetric tensor gauge field theories on Minkowski space-time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.Comment: LaTeX, 24 pages, no figure. One reference added and one definition corrected. Accepted for publication in NP

The continuous spin limit of higher spin field equations

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity with their product being fixed. The result allows to transform the Wigner equations to a gauge invariant Fronsdal-like form. We also give the generalisation of the Wigner equations to higher dimensions with fields belonging to arbitrary representations of the massless little group.Comment: 18 pages, JHEP style. Typos corrected, references adde

Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.Comment: the bug with symbol $\bar\Box$ is fixe

How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples

Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic higher-derivative vertices in constantly curved backgrounds. Finally we outline how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives).Comment: LaTeX, 50 pages, minor changes, many refs added; version accepted for publication in Reviews of Modern Physic

No Self-Interaction for Two-Column Massless Fields

We investigate the problem of introducing consistent self-couplings in free theories for mixed tensor gauge fields whose symmetry properties are characterized by Young diagrams made of two columns of arbitrary (but different) lengths. We prove that, in flat space, these theories admit no local, Poincar\'e-invariant, smooth, self-interacting deformation with at most two derivatives in the Lagrangian. Relaxing the derivative and Lorentz-invariance assumptions, there still is no deformation that modifies the gauge algebra, and in most cases no deformation that alters the gauge transformations.Our approach is based on a BRST-cohomology deformation procedure.Comment: 41 pages, LaTe

How do Regimes Affect Asset Allocation?

International equity returns are characterized by episodes of high volatility and unusually high correlations coinciding with bear markets. We develop models of asset returns that match these patterns and use them in asset allocation. First, the presence of regimes with different correlations and expected returns is difficult to exploit within a framework focused on global equities. Nevertheless, for all-equity portfolios, a regime-switching strategy dominates static strategies out-of-sample. Second, substantial value is added when an investor chooses between cash, bonds and equity investments. When a persistent bear market hits, the investor switches primarily to cash. There are large market timing benefits because the bear market regimes tend to coincide with periods of relatively high interest rates.

Notes on conformal invariance of gauge fields

In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.Comment: 38 page