Higher Spin Fields Research Articles

Addendum to: BRST approach to Lagrangian formulation for mixed-symmpetry fermionic higher-spin fields

Addendum to: BRST approach to Lagrangian formulation for mixed-symmpetry fermionic higher-spin fields

Spinning particles and higher spin field equations

Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac quantization scheme the field equations emerge as Dirac constraints on the Hilbert space, and we outline how they lead to the description of higher spin fields in terms of the more standard Fronsdal-Labastida equations. Then, we describe how these actions can be extended so that the propagating particle is allowed to take different values of the spin, i.e. carry a reducible representation of the Poincaré group. This way one may identify a four dimensional model that carries the same degrees of freedom of the minimal Vasiliev’s interacting higher spin field theory. Extensions to massive particles and to propagation on (A)dS spaces are also briefly commented upon.

Comments on spinning OPE blocks in AdS3/CFT2

We extend the work of [48], [49], to obtain an integral expression of OPE blocks for spinning primaries in CFT2. We observe, when the OPE blocks are made out of conserved spinning primaries, the integral becomes a product of two copies of weighted AdS2 fields, smeared along geodesics. In this way, conserved current OPE blocks in CFT2 have a different representation in terms of AdS2 geodesic operators, in stead of viewing them as AdS3 geodesic operators. We also show, how this representation can be related to AdS3 massless higher spin fields through HKLL bulk field reconstruction. Using this picture, we consistently obtain the closed form expression of four point spinning conformal block as a product of two AdS2 Geodesic Witten diagrams.

Minimal gauge invariant and gauge fixed actions for massive higher-spin fields

Inspired by the rich structure of covariant string field theory, we propose a minimal gauge invariant action for general massive integer spin n field. The action consists of four totally symmetric tensor fields of order respectively n, n − 1, n − 2 and n − 3, and is invariant under the gauge transformation represented by two also totally symmetric fields of order n − 1 and n − 2. This action exactly has the same gauge structure as for the string field theory and we discuss general covariant gauge fixing procedure using the knowledge of string field theory. We explicitly construct the corresponding gauge fixed action for each of general covariant gauge fixing conditions.

AdS maps and diagrams of bi-local holography

We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality.

HS in flat spacetime: the effective action method

This is the first paper in a series of three dealing with HS theories in flat spacetime. It is divided in three parts. The first part is an elaboration on the method of effective action, initiated in a previous paper. We study the properties of correlators of currents in the free fermion coupled to external higher spin (HS) potentials, and develop techniques for their explicit calculation. In particular we show how they can be calculated via ordinary Feynman diagram techniques. We also introduce the concept of curvedL_infty algebra and show how it can be realized in the context of the fermion model. In part II we compare the results of the scalar model and those of the fermion model (coupled to HS fields). We show that the HS field formulation coming from the scalar model is the ‘square’ of the one ensuing from the fermion model. Finally, in part III, we analyse the possible obstructions that one may meet in constructing the effective action: these are the analogues of anomalies in ordinary gauge theories. We provide explicit and compact formulas of the latter.

Coupling coefficient in three dimensional higher spin holography

We consider linearised Vasiliev's equations around the background AdS field in three dimensions for the scalar-scalar-higher spin field correlation function. Relating this with the higher spin field determined in the metric formulation allows determination of the corresponding coupling coefficient. The result agrees with the analogous computation for the spin three field.

Formal Higher Spin Gravities

We present a complete solution to the problem of Formal Higher Spin Gravities — formally consistent field equations that gauge a given higher spin algebra and describe free higher spin fields upon linearization. The problem is shown to be equivalent to constructing a certain deformation of the higher spin algebra as an associative algebra. Given this deformation, all interaction vertices are explicitly constructed. All formal solutions of the equations are explicitly described in terms of an auxiliary Lax pair, the deformation parameter playing the role of the spectral one. We also discuss a natural set of observables associated to such theories, including the holographic correlation functions. As an application, we give another form of the Type-B formal Higher Spin Gravity and discuss a number of systems in five dimensions.

Electric-Magnetic Duality in Gravity and Higher-Spin Fields

Over the past two decades, electric-magnetic duality has made significant progress in linearized gravity and higher spin gauge fields in arbitrary dimensions. By analogy with Maxwell theory, the Dirac quantization condition has been generalized to both the conserved electric-type and magnetic-type sources associated with gravitational fields and higher spin fields. The linearized Einstein equations in $D$ dimensions, which are expressed in terms of the Pauli-Fierz field of the \textit{graviton} described by a 2nd-rank symmetric tensor, can be dual to the linearized field equations of the \textit{dual graviton} described by a Young symmetry $(D-3, 1)$ tensor. Hence, the dual formulations of linearized gravity are written by a 2nd-rank symmetric tensor describing the Pauli-Fierz field of the dual graviton in $D=4$, while we have the Curtright field with Young symmetry type $(2,1)$ in $D=5$. The equations of motion of spin-$s$ fields ($s>2$) described by the generalized Fronsdal action can also be dualized to the equations of motion of dual spin-$s$ fields. In this review, we focus on dual formulations of gravity and higher spin fields in the linearized theory, and study their SO(2) electric-magnetic duality invariance, twisted self-duality conditions, harmonic conditions for wave solutions, and their configurations with electric-type and magnetic-type sources. Furthermore, we briefly discuss the latest developments in their interacting theories.

Higher spin theories in flat space–time

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

A Spin‐2 Conjecture on the Swampland

AbstractWe consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the Stückelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further evidence for the conjecture from string theory.

On the structure of the conformal higher-spin wave operators

We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t ≤ s. In the case of the usual Fradkin-Tseytlin fields t = 1 this gives a systematic derivation of the factorization formulas known in the literature while for t > 1 the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.

Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

We introduce prepotentials for fermionic higher-spin gauge fields in four space-time dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in three dimensions. This is necessary because the prepotentials turn out to be three-dimensional fields that enjoy both “higher-spin diffeomorphism” and “higher-spin Weyl” gauge symmetries. We discuss a number of the key properties of the relevant Cotton tensors. The reformulation of the equations of motion as “twisted self-duality conditions” is then exhibited. We show next how the Hamiltonian constraints can be explicitly solved in terms of appropriate prepotentials and show that the action takes then the same remarkable form for all spins.

Higher-Spin Gauge Theories and Bulk Locality.

We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti-de Sitter space-times. We show that there is a nonlocal obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal program for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could potentially lie beyond the framework of classical field theory.

Topologically massive higher spin gauge theories

We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer n > 2 we introduce a conformal spin- frac{n}{2} gauge field {h}_{(n)}={h}_{alpha_1dots {alpha}_n} (with n spinor indices) of dimension (2 − n/2) and argue that it possesses a Weyl primary descendant C(n) of dimension (1 + n/2). The latter proves to be divergenceless and gauge invariant in any conformally flat space. Primary fields C(3) and C(4) coincide with the linearised Cottino and Cotton tensors, respectively. Associated with C(n) is a Chern-Simons-type action that is both Weyl and gauge invariant in any conformally flat space. These actions, which for n = 3 and n = 4 coincide with the linearised actions for conformal gravitino and conformal gravity, respectively, are used to construct gauge-invariant models for massive higher-spin fields in Minkowski and anti-de Sitter space. In the former case, the higher-derivative equations of motion are shown to be equivalent to those first-order equations which describe the irreducible unitary massive spin- frac{n}{2} representations of the 3D Poincaré group. Finally, we develop mathcal{N}=1 supersymmetric extensions of the above results.

Constrained BRST-BFV Lagrangian formulations for higher spin fields in Minkowski spaces

BRST-BFV method to construct constrained Lagrangian formulations for (ir)reducible half-integer higher-spin Poincare group representations in Minkowski space is suggested. The procedure is derived by two ways: first, from the unconstrained BRST-BFV method for mixed-symmetry higher-spin fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in Nucl. Phys.B 869 (2013) 523, arXiv:1211.1273) by extracting the second-class constraints subsystem, Ôα = (Ôa, Ôa+), from a total super-algebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, Ôa. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST operator QC and spin operators σCi . The closedness of the superalgebra {QC, Ôa, σCi} guarantees that the final gauge-invariant Lagrangian formulation is compatible with the off-shell algebraic constraints Ôa imposed on the field and gauge parameter vectors of the Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to Ôa, in comparison with the vectors for unconstrained BRST-BFV Lagrangian formulation. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained Lagrangian formulations for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with the Fang-Fronsdal formulation for totally-symmetric HS field with respective off-shell gamma-traceless constraints. The triplet and unconstrained quartet Lagrangian formulations for the latter field are derived. The constrained BRST-BFV methods without off-shell constraints describe reducible half-integer HS Poincare group representations with multiple spins as a generalized triplet and provide a starting point for constructing unconstrained Lagrangian formulations by using the generalized quartet mechanism. A gauge-invariant Lagrangian constrained description for a massive spin-tensor field of spin n + 1/2 is obtained using a set of auxiliary Stueckelberg spin-tensors. A concept of BRST-invariant second-class constraints for dynamical systems with mixed-class constraints is suggested, leading to equivalent (w.r.t. the BRST-BFV prescription) results of quantization both at the operator level and in terms of the partition function.

On Lagrangian Construction of Massive Higher Spins Supermultiplets in 3D AdS

We give the component Lagrangian construction of the on-shell $$\mathcal{N} = 1$$ massive higher spin supermultiplets in three dimensional (3D) anti de Sitter ( $$AdS$$ ) space. The approach is based on the frame-like gauge invariant formulation, where massive higher spin fields are realized through a system of massless ones. We construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge invariant objects (curvatures) in the process of their consistent supersymmetric deformation.

Detecting higher spin fields through statistical anisotropy in the CMB bispectrum

Inflation may provide a suitable collider to probe physics at very high energies. In this paper we investigate the impact on the CMB bispectrum of higher spin fields which are long-lived on super-Hubble scales, e.g. partially massless higher spin fields. We show that distinctive statistical anisotropic signals on the CMB three-point correlator are induced and we investigate their detectability.

Nonminimal coupling contribution to DIS at low x in Holographic QCD

We consider the effect of including a non-minimal coupling between a $U(1)$ vector gauge field and the graviton Regge trajectory in holographic QCD models. This coupling describes the QCD interaction between the quark bilinear electromagnetic current and the Pomeron. We test this new coupling against DIS data at low Bjorken $x$ and obtain an excellent fit with a chi squared of 1.1 over a very large kinematical range in the photon virtuality $Q^2<400 \ {\rm GeV}^2$ and for $x<10^{-2}$. The scale of the new dimension full coupling, which arises from integrating higher spin fields, is of order $6\ {\rm GeV}$. This value matches precisely the expectations from effective field theory, which indicate that such corrections are controlled by the mass gap between the spin two and spin four glueballs that are described holographically by the graviton and spin four field in the graviton Regge trajectory, respectively

Induced actions for higher spin fields

We have calculated two-point correlators of higher spin currents, with spins up to six, in free massive QFT’s with scalar and Dirac fields in D = 3,4,5,6 spacetime dimensions. The infrared and ultraviolet limits are analysed, with the motivation for improving our understanding of the interacting higher spin theories.