Hamiltonian analysis and positivity of a newmassive spin-2 model

Recently a new model has been proposed to describe free massive spin-2 particles in D dimensions in terms of a non symmetric rank-2 tensor eµν and a mixed symmetry tensor Bµ[αβ]. The model is invariant under linearized diffeomorphisms without Stueckelberg fields. It resembles a spin-2 version of the topologically massive spin-1 BF model (Cremmer-Scherk model). Here we apply the Dirac-Bergmann procedure in order to identify all Hamiltonian constraints and perform a complete counting of degrees of freedom. In D = 3 + 1 we find 5 degrees of freedom corresponding to helicities ±2, ±1, 0 as expected. The positivity of the reduced Hamiltonian is proved by using spin projection operators. We have also proposed a parent action that establishes the duality between the Fierz-Pauli and the new model. The equivalence between gauge invariant correlation functions of both theories is demonstrated.

Extracting bigravity from string theory

The origin of the graviton from string theory is well understood: it corresponds to a massless state in closed string spectra, whose low-energy effective action, as extracted from string scattering amplitudes, is that of Einstein-Hilbert. In this work, we explore the possibility of such a string-theoretic emergence of ghost-free bimetric theory, a recently proposed theory that involves two dynamical metrics, that around particular backgrounds propagates the graviton and a massive spin-2 field, which has been argued to be a viable dark matter candidate. By choosing to identify the latter with a massive spin-2 state of open string spectra, we compute tree-level three-point string scattering amplitudes that describe interactions of the massive spin-2 with itself and with the graviton. With the mass of the external legs depending on the string scale, we discover that extracting the corresponding low-energy effective actions in four spacetime dimensions is a subtle but consistent process and proceed to appropriately compare them with bimetric theory. Our findings consist in establishing that string and bimetric theory provide to lowest order the same set of two-derivative terms describing the interactions of the massive spin-2 with itself and with the graviton, albeit up to numerical coefficient discrepancies, a fact that we analyze and interpret. We conclude with a mention of future investigations.

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 $$ \mathcal{N} $$ 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.

Cheeger bounds on spin-two fields

We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The argument involves a recently-noticed relation to Bakry-Émery geometry, a version of the so-called Cheeger constant, and the theory of synthetic Ricci lower bounds. The latter technique allows generalizations to non-smooth spaces such as those with D-brane singularities. For AdSd vacua with a bridge admitting an AdSd+1 interpretation, the holographic dual is a CFTd with two CFTd−1 boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for d = 4. We also prove new bounds on the higher eigenvalues. These are in agreement with the spin-two swampland conjecture in the regime where the background is scale-separated; in the opposite regime we provide examples where they are in naive tension with it.

Dark matter interacting via a massive spin-2 mediator in warped extra-dimensions

We study dark matter interacting via a massive spin-2 mediator. To have a consistent effective theory for the spin-2 particle, we work in a warped extra-dimensional model such that the mediator(s) are the Kaluza-Klein (KK) modes of the 5D graviton. We pay close attention to dark matter annihilations into KK-gravitons. Due to the high energy behavior of longitudinal modes of spin-2 fields, these channels exhibit a tremendous growth at large center of mass energies $$ \sqrt{s} $$ s if only one spin-2 mediator is considered. For the first time, we include the full KK-tower in this dark matter production process and find that this growth is unphysical and cancels once the full field content of the extra-dimensional theory is taken into account. Interestingly, this implies that it is not possible to approximate the results obtained in the full theory with a reduced set of effective interactions once $$ \sqrt{s} $$ s is greater than the first graviton mass. This casts some doubt on the universal applicability of previous studies with spin-2 mediators within an EFT framework and prompts us to revisit the phenomenological allowed parameter space of gravitationally interacting scalar dark matter in warped extra-dimensions.

Spinning amplitudes from scalar amplitudes

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin J exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.

Dark matter self-interactions from spin-2 mediators

We propose a new mechanism for rendering dark matter self-interacting in the presence of a massive spin-2 mediator. The derived Yukawa-type potential for dark matter is independent of the spins of dark matter in the leading order of the momentum expansion, so are the resulting non-perturbative effects for the dark matter self-scattering. We find that both the Born cross section and relatively mild resonance effects assist to make the self-scattering cross section velocity-dependent. We discuss how to evade the current indirect bounds on dark matter annihilations and show that the model is marginally compatible with perturbative unitarity in the ghost-free realization of the massive spin-2 particle.

Kaluza-Klein from colour-kinematics duality for massive fields

We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.