Massive Higher Spin Fields Research Articles

Symmetric vs. chiral approaches to massive fields with spin

Abstract Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance.

On massive higher spin supermultiplets in d = 4

In this work we discuss the cubic interactions for massless spin 3/2 gravitino with massive higher spin supermultiplets using three superblocks (2, 3/2), (5/2, 2) and (3, 5/2) as the first non-trivial examples. We use gauge invariant formalism for the massive higher spin fields and, as is common in such cases, we face an ambiguity related with the possible field redefinitions due to the presence of Stueckelberg fields. From one hand, we show how this ambiguity can be used as one more way to classify possible cubic vertices. We also note that all these field redefinitions do not change the part of the Lagrangian which appears in the unitary gauge (where all Stueckelberg fields are set to zero) so we still have some important independent results. From the other hand, we show how using the so-called unfolded formalism one can fix these ambiguities and obtain consistent deformations for all massive field gauge invariant curvatures which is the most important step in the Fradkin-Vasiliev formalism. Unfortunately, this works for the massive fields only so the way to construct deformations for the massless field curvatures is still has to be found.

Massive spin three-half field in a constant electromagnetic background

Massive higher-spin fields are difficult to introduce consistent interactions, including electromagnetic and gravitational ones which are clearly exhibited by (non-elementary) higher-spin particles in nature. We construct an action that describes consistent interactions of massive spin three-half field with a constant electromagnetic background. We also work out the relation to the chiral approach.

Compton Amplitude for Rotating Black Hole from QFT.

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin s=0,1/2,1,…,∞, from which we extract the corresponding classical amplitude to all orders in the spin vector S^{μ}. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-s Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin.

Cubic action for spinning black holes from massive higher-spin gauge symmetry

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic amplitude of Arkani-Hamed-Huang-Huang. The same is achieved for the root-Kerr theory, i.e. for the minimal electromagnetic interaction of a massive higher-spin field.

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; two massive, both with coinciding and with different masses and one massless field of spins s1,s2,s3. Unlike the previous results on cubic vertices we extend our earlier result in (Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470) for massless fields and employ the complete BRST operator, including the trace constraints, which is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contains the additional terms with a smaller number of space-time derivatives. We prove that without traceless conditions for the cubic vertices in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangians for the massive spin of the s field and the massless scalars, both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive spin s with massless scalar and vector fields and with two vector fields; massless helicity λ with massless scalar and massive vector fields; two massive fields of spins s, 0 and massless scalar is also considered.

Gauge-Invariant Lagrangian Formulations for Mixed-Symmetry Higher-Spin Bosonic Fields in AdS Spaces

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux Y(s1,…,sk) with k≥2 rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a k=2 Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic sp(2k) algebra used for mixed-symmetry HS fields in flat spaces [Buchbinder, I.L.; et al. Nucl. Phys. B 2012, 862, 270–326]. Polynomial deformations of the su(1,1) algebra related to the Bethe ansatz are studied as a byproduct. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for Y(s1,s2) is found, with non-vanishing terms (resolving the Jacobi identities) of the third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin (s1,s2) is deduced. Following the results of [Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470.; Buchbinder, I.L.; et al. arXiv 2022, arXiv:2212.07097], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields (being candidates for massive particles in the Dark Matter problem). A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin (1,1) is obtained.

Spin supplementary condition in quantum field theory: covariant SSC and physical state projection

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the projection conditions on polarisation tensors, which remove timelike/longitudinal polarisations from the physical spectrum. The claim is supported by three examples of massive spinning particles coupled to electromagnetism: Dirac and Proca fields in quantum field theory, and \U0001d4a9 = 1 worldline QFT for classical worldline theory. This suggests a resolution to the apparent discrepancy between effective field theory description of massive higher-spin fields [1, 2] and post-Newtonian effective field theory of spinning classical particles [3], where the former admits more unfixed parameters compared to the latter; the additional parameters are fixed by projection conditions and therefore are not tunable parameters.

Unfolded Fierz-Pauli equations in three-dimensional asymptotically flat spacetimes

We utilise a quotient of the universal enveloping algebra of the Poincaré algebra in three spacetime dimensions, on which we formulate a covariant constancy condition. The equations so obtained contain the Fierz-Pauli equations for non-interacting, massive higher-spin fields, and can thus be regarded as an unfolding of the Fierz-Pauli system. All fundamental fields completely decouple from each other. In the non-truncated case, the field content includes infinitely many copies of each field at fixed spin.

Chiral Approach to Massive Higher Spins.

We propose a new, chiral description for massive higher-spin particles in four spacetime dimensions, which facilitates the introduction of consistent interactions. As proof of concept, we formulate three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory, or gravity. The theories are chiral and have simple Lagrangians, resulting in Feynman rules analogous to those of massive scalars. Starting from these Feynman rules, we derive tree-level scattering amplitudes with two higher-spin matter particles and any number of positive-helicity photons, gluons, or gravitons. The amplitudes reproduce the arbitrary-multiplicity results that were obtained via on-shell recursion in a parity-conserving setting, and which chiral and nonchiral theories thus have in common. The presented theories are currently the only examples of consistent interacting field theories with massive higher-spin fields.

Supersymmetric quantum chiral higher spin gravity

We study quantum properties of supersymmetric mathcal{N} = 1 and mathcal{N} = 4 extensions of the four dimensional bosonic Chiral Higher Spin Gravities (HiSGRAs). We discuss the spectra, the classical actions and define the Feynman rules in mathcal{N} = 1 and mathcal{N} = 4 superspaces in the light-front gauge. Using these Feynman rules, we compute tree and one-loop amplitudes for these systems. A dimensional reduction to a system with mathcal{N} = 2 supersymmetry and with massive higher spin fields is performed and quantum properties of this system are discussed.

Higher-spin states of the superstring in an electromagnetic background

Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest mathcal{N} = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.

Lagrangian BRST formulation of massive higher-spin fields of the general symmetry type

Lagrangian BRST formulation of massive higher-spin fields of the general symmetry type

Stringlike theory in three dimensions and massive higher spins

An example of a consistent theory with massive higher spin fields is constructed in flat space-time of dimension three. The action is written in the light-cone gauge. The theory has certain stringy features, e.g. its spectrum is unbounded in spin and mass, the theory admits Chan-Paton factors. The quartic and the higher tree-level amplitudes vanish, which softens the UV behaviour at the loop level and provides a new mechanism of how massive higher spin states can resolve the Quantum Gravity Problem.

Matter couplings and equivalence principles for soft scalars

Scalar effective field theories with enhanced soft limits behave in many ways like gauge theories and gravity. In particular, symmetries fix the structure of interactions and the tree-level S-matrix in both types of theories. We explore how this analogy persists in the presence of matter by considering theories with additional fields coupled to the Dirac-Born-Infeld (DBI) scalar or the special galileon in a way that is consistent with their symmetries. Using purely on-shell arguments, we show that these theories obey analogues of the S-matrix equivalence principle whereby all matter fields must couple to the DBI scalar or the special galileon through a particular quartic vertex with a universal coupling. These equivalence principles imply the universality of the leading double soft theorems in these theories, which are scalar analogues of Weinberg’s gravitational soft theorem, and can be used to rule out interactions with massless higher-spin fields when combined with analogues of the generalized Weinberg-Witten theorem. We verify in several examples that amplitudes with external matter fields nontrivially exhibit enhanced single soft limits and we show that such amplitudes can be constructed using soft recursion relations when they have sufficiently many external DBI or special galileon legs, including amplitudes with massive higher-spin fields. As part of our analysis we construct a recently conjectured special galileon-vector effective field theory.

Massive higher spin fields in the frame-like multispinor formalism

In this paper, a gauge invariant description of massive higher spin bosonic and fermionic particles in frame-like Lagrangian and unfolded formalism in (A)dS4 is built. A complete set of gauge invariant object is also constructed and the Lagrangian is rewritten in terms of these objects. The unitarity of the theories is studied alongside with the partially massless limits. The calculations are carried out in the multispinor formalism, which simplifies them and is particularly convenient for the supersymmetry studies.

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.

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.

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.

Large-scale messengers from massive higher spin fields

We show that nonperturbative production of massive higher spin fields from vacuum will accompany the generation of non-vanishing macroscopic energy-momentum tensor correlators. This argument is based on the general causal field formalism, which gives a manifestly covariant description of higher spin particles without any reference to gauge redundancy. Our findings are direct consequence of the Poincaré covariance and anlayticity of the Green’s functions and independent of any detailed particle physics model. Further, we discuss the idea that any mechanism causing imbalance between the on-shell production of left- and right-handed fields leads to a helical structure in the energy momentum correlators and violation of the macroscopic parity symmetry. We check our method for fields with spin frac{1}{2} and show that it correctly reproduces previous results. The formalism, however, suffers from pathologies related to non-localities that appear for massless particles with spin ≥ 1 in flat space. We discuss the origin of these pathologies and the relevance of our findings to cosmology.