Per Sundell

Biaxially symmetric solutions to 4D higher spin gravity

We review some aspects of biaxially symmetric solutions to Vasiliev?s equations in four-dimensional spacetime with a negative cosmological constant. The solutions, which activate bosonic fields of all spins, are constructed using gauge functions, projectors and deformed oscillators. The deformation parameters, which are formally gauge invariant, are related to generalized electric and magnetic charges in asymptotic weak-field regions. Alternatively, the solutions can be characterized in a dual fashion using 0-form charges which are higher spin Casimir invariants built from combinations of curvatures and all their derivatives that are constant on shell and well-defined everywhere.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Higher spin theories and holography?.

Massless Higher Spins and Holography

Abstract We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R . The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consistent truncation to massless HS fields. A survey of massless HS theories with 32 supersymmetries in D =4,5,7 (where the 7D results are new) is given and the corresponding composite operators are discussed. In the case of AdS 4 , the cubic couplings of a minimal bosonic massless HS gauge theory are described. We examine high energy/small tension limits giving rise to massless HS fields in the type IIB string on AdS 5 × S 5 and M-theory on AdS 4/7 × S 7/4 . We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS 5 × S 5 and AdS 4 × S 7 where the HS symmetry is broken by finite g YM . In AdS 5 × S 5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g YM 2 =0 corresponds to a critical string tension of order 1/ R 2 and a finite string coupling of order 1/ N . In AdS 7 × S 4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the A N −1 (2,0) SCFT, expandable in terms of operators with anomalous dimensions that are asymptotically small for large spin. The minimal energy configurations have semi-classical energy E = s for all s and the geometry of infinitely stretched strings with energy and spin density concentrated at the endpoints.

The Dirichlet super-p-branes in ten-dimensional type IIA and IIB supergravity

We give the full supersymmetric and kappa-symmetric actions for the Dirichlet p-branes, including their coupling to background superfields of ten-dimensional type IIA and IIB supergravity.

On the uniqueness of minimal coupling in higher-spin gauge theory

We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasilievs cubic 2?s?s vertex, which contains up to 2s?2 derivatives dressed by a cosmological constant ?, has a limit where: (i) ????0; (ii) the spin-2 Weyl tensor scales non-uniformly with s; and (iii) all lower-derivative couplings are scaled away. For s = 3 the limit yields the unique non-abelian spin 2?3?3 vertex found recently by two of the authors, thereby proving the uniqueness of the corresponding FV vertex. We extend the analysis to s = 4 and a class of spin 1?s?s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with ? = 0 but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with ??0, wherein the standard minimal couplings mediated via the Lorentz connection are subleading at energy scales (|?|)1/2??E??Mp. Finally, combining our results with those obtained by Metsaev, we give the complete list of all the manifestly covariant cubic couplings of the form 1?s?s? and 2?s?s?, in Minkowski background.

Doubletons and 5D higher spin gauge theory

We use Grassmann even spinor oscillators to construct a bosonic higher spin extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and show that the gauging of hs(2,2) gives rise to a spectrum of physical massless fields with spin s = 0,2,4,... that is a UIR of hs(2,2). In addition to a master gauge field which contains the massless s = 2,4,... fields, we construct a scalar master field containing the massless s = 0 field, the generalized Weyl tensors and their derivatives. We give the appropriate linearized constraint on this master scalar field, which together with a linearized curvature constraint produces the correct linearized field equations. A crucial step in the construction of the theory is the identification of a central generator K which is eliminated by means of a coset construction. Its charge vanishes in the spectrum , which is the symmetric product of two spin zero doubletons. We expect our results to pave the way for constructing an interacting theory whose curvature expansion is dual to a CFT based on higher spin currents formed out of free doubletons in the large-N limit. Thus, extending a recent proposal of Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory describes a truncation of the bosonic massless sector of tensionless type-IIB string theory on AdS5 × S5 for large N. This implies AdS/CFT correspondence in a parameter regime where both boundary and bulk theories are perturbative.

Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism

We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.

An action principle for Vasiliev’s four-dimensional higher spin gravity

We provide Vasilievs fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle. We first extend Vasilievs original system with differential forms in degrees higher than 1. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: one, a set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and the other, a set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of rank 2 or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on-shell, to Vasilievs original system.

Structure and thermodynamic stability of hydrogen interstitials in BaZrO3 perovskite oxide from density functional calculations

Density functional calculations have been used to study the electronic structure, preferred sites in the lattice, formation energies and vibrational frequencies for hydrogen interstitials in different charge states in the cubic phase of perovskite-structured BaZrO3. By combining ab initio results with thermodynamic modeling, defect formation at finite temperature and pressure has been investigated. We demonstrate how the site selectivity and spatial distribution of dopant atoms in the lattice can be affected by changes in the environmental conditions (atomic chemical potentials, oxygen partial pressure and temperature) used during processing of the material. In addition, we have calculated the thermodynamic parameters of the water uptake reaction for an acceptor-doped BaZrO3 crystal in equilibrium with a humid atmosphere. The interaction energies between a protonic defect and the investigated Ga, Gd, In, Nd, Sc, and Y dopants were found to be attractive, and we show that a simple model of defect association may reproduce an experimentally observed trend in the hydration enthalpy.

Unfolding mixed-symmetry fields in AdS and the BMV conjecture: II. Oscillator realization

Following the general formalism presented in arXiv:0812.3615 — referred to as Paper I — we derive the unfolded equations of motion for tensor fields of arbitrary shape and mass in constantly curved backgrounds by radial reduction of Skvortsovs equations in one higher dimension. The complete unfolded system is embedded into a single master field, valued in a tensorial Schur module realized equivalently via either bosonic (symmetric basis) or fermionic (anti-symmetric basis) vector oscillators. At critical masses the reduced Weyl zero-form modules become indecomposable. We explicitly project the latter onto the submodules carrying Metsaevs massless representations. The remainder of the reduced system contains a set of Stuckelberg fields and dynamical potentials that leads to a smooth flat limit in accordance with the Brink-Metsaev-Vasiliev (BMV) conjecture. In the unitary massless cases in AdS, we identify the Alkalaev-Shaynkman-Vasiliev frame-like potentials and explicitly disentangle their unfolded field equations.

An exact solution of 4D higher-spin gauge theory

We give a one-parameter family of exact solutions to 4D higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via two dS3-foliated domain walls and two H3-foliated Robertson–Walker spacetimes—one in the future and one in the past—with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants.