A compendium of sphere path integrals

We study the manifestly covariant and local 1-loop path integrals on Sd+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

AdS (super)projectors in three dimensions and partial masslessness

We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS3. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group SO(2, 2) of AdS3. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS3 into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to irreducible representations of SO(2, 2). Our results are then extended to the case of $$ \mathcal{N} $$ N = 1 AdS3 supersymmetry.

On the consistency of (partially-)massless matter couplings in de Sitter space

We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in (d + 1)-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary. Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-J. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-J field can couple. 4-point Ward-Takahashi identities then constrain the corresponding cubic couplings. For massless spinning fields, we show that Weinberg’s flat space results carry over to (d+1)-dimensional de Sitter space: for spins J = 1, 2 gauge-invariance implies charge-conservation and the equivalence principle while, assuming locality, higher-spins J > 2 cannot couple consistently to scalar matter. This result also applies to anti-de Sitter space. For partially-massless fields, restricting for simplicity to those of depth-2, we show that there is no consistent coupling to scalar matter in local theories. Along the way we also give a detailed account of how contact amplitudes with and without derivatives are represented in the Mellin-Barnes representation. Various new explicit expressions for 3- and 4-point functions involving (partially-)massless fields and conformally coupled scalars in dS4 are given.

AdS3/AdS2 degression of massless particles

We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

Bulk reconstruction and Bogoliubov transformations in AdS2

In the bulk reconstruction program, one constructs boundary representations of bulk fields. We investigate the relation between the global/Poincare and AdS-Rindler representations for AdS2. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.

Kalb-Ramond backgrounds in α′-complete cosmology

We study the matter-coupled equations of motion for cosmological NS massless fields including all α′ corrections in an O(d, d) duality invariant approach, with emphasis on the Kalb-Ramond two-form field B(2) and its source. Solutions for the vacuum and matter cases are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for B(2) required by the duality invariant framework implies that the two-form is non-isotropic.

The σ− Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ− cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in AdS4. In the d-dimensional case Hp(σ−) is computed for any p and interpretation of Hp(σ−) is given both for the original Fronsdal system and for the associated systems of higher form fields.

Perturbation analysis for massless spin fields in accelerating Kerr-Newman-(anti-)de Sitter black holes

We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.

$$ \mathcal{N} $$ = 2 supersymmetric partially massless fields and other exotic non-unitary superconformal representations

We find and classify the simplest $$ \mathcal{N} $$ N = 2 SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying representations of the $$ \mathcal{N} $$ N = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the $$ \mathcal{N} $$ N = 1 case, the simplest $$ \mathcal{N} $$ N = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that $$ \mathcal{N} $$ N = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s − 2.