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Register a new userMassive Spin-2 Scattering and Asymptotic Superluminality
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We place model-independent constraints on theories of massive spin-2 particles by considering the positivity of the phase shift in eikonal scattering. The phase shift is an asymptotic $S$-matrix observable, related to the time delay/advance experienced by a particle during scattering. Demanding the absence of a time advance leads to constraints on the cubic vertices present in the theory. We find that, in theories with massive spin-2 particles, requiring no time advance means that either: (i) the cubic vertices must appear as a particular linear combination of the Einstein-Hilbert cubic vertex and an $h_{mu u}^3$ potential term or (ii) new degrees of freedom or strong coupling must enter at parametrically the mass of the massive spin-2 field. These conclusions have implications for a variety of situations. Applied to theories of large-$N$ QCD, this indicates that any spectrum with an isolated massive spin-2 at the bottom must have these particular cubic self-couplings. Applied to de Rham-Gabadadze-Tolley massive gravity, the constraint is in accord with and generalizes previous results obtained from a shockwave calculation: of the two free dimensionless parameters in the theory there is a one parameter line consistent with a subluminal phase shift.
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We constrain theories of a massive spin-2 particle coupled to a massless spin-2 particle by demanding the absence of a time advance in eikonal scattering. This is an $S$-matrix consideration that leads to model-independent constraints on the cubic vertices present in the theory. Of the possible cubic vertices for the two spin-2 particles, the requirement of subluminality leaves a particular linear combination of cubic vertices of the Einstein--Hilbert type. Either the cubic vertices must appear in this combination or new physics must enter at a scale parametrically the same as the mass of the massive spin-2 field. These conclusions imply that there is a one-parameter family of ghost-free bimetric theories of gravity that are consistent with subluminal scattering. When both particles couple to additional matter, subluminality places additional constraints on the matter couplings. We additionally reproduce these constraints by considering classical scattering off of a shockwave background in the ghost-free bimetric theory.
We consider scattering of massless higher-spin particles in the eikonal regime in four dimensions. By demanding the absence of asymptotic superluminality, corresponding to positivity of the eikonal phase, we place constraints on the possible cubic couplings which can appear in the theory. The cubic couplings come in two types: lower-derivative non-abelian vertices, and higher-derivative abelian vertices made out of gauge-invariant curvature tensors. We find that the abelian couplings between massless higher spins lead to an asymptotic time advance for certain choices of polarizations, indicating that these couplings should be absent unless new states come in at the scale suppressing the derivatives in these couplings. A subset of non-abelian cubic couplings are consistent with eikonal positivity, but are ruled out by consistency of the four-particle amplitude away from the eikonal limit. The eikonal constraints are therefore complementary to the four-particle test, ruling out even trivial cubic curvature couplings in any theory with a finite number of massless higher spins and no new physics at the scale suppressing derivatives in these vertices.
We derive analyticity constraints on a nonlinear ghost-free effective theory of a massive spin-2 particle known as pseudo-linear massive gravity, and on a generalized theory of a massive spin-1 particle, both of which provide simple IR completions of Galileon theories. For pseudo-linear massive gravity we find that, unlike dRGT massive gravity, there is no window of parameter space which satisfies the analyticity constraints. For massive vectors which reduce to Galileons in the decoupling limit, we find that no two-derivative actions are compatible with positivity, but that higher derivative actions can be made compatible.
Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process.
We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrodinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number $L=1$ in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.
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