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Register a new userBlack hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime
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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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We diagram the behavior of 5-dimensional anti-de Sitter spacetime against horizon formation in the gravitational collapse of a scalar field, treating the scalar field mass and width of initial data as free parameters, which we call the stability phase diagram. We find that the class of stable initial data becomes larger and shifts to smaller widths as the field mass increases. In addition to classifying initial data as stable or unstable, we identify two other classes based on nonperturbative behavior. The class of metastable initial data forms a horizon over longer time scales than suggested by the lowest order perturbation theory at computationally accessible amplitudes, and irregular initial data can exhibit non-monotonic and possibly chaotic behavior in the horizon formation times. Our results include evidence for chaotic behavior even in the collapse of a massless scalar field.
We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in $left(d+1right)$-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 Weinbergs flat space results carry over to $left(d+1right)$-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 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 dS$_4$ are given.
We construct five dimensional black rings in global anti-de Sitter space using numerical methods. These rings satisfy the BPS bound $| J | < M ell$, but the angular velocity always violates the Hawking-Reall bound $| Omega_H ell | leq 1$, indicating that they should be unstable under superradiance. At high temperatures, the limit $| Omega_H ell | searrow 1$ is attained by thin rings with an arbitrarily large radius. However, at sufficiently low temperatures, this limit is saturated by a new kind of rings, whose outer circle can still be arbitrarily long while the hole in the middle does not grow proportionally. This gives rise to a membrane-like horizon geometry, which does not have an asymptotically flat counterpart. We find no evidence for thin AdS black rings whose transverse $S^2$ is much larger than the radius of AdS, $ell$, and thus these solutions never fall into the hydrodynamic regime of the dual CFT. Thermodynamically, we find that AdS black rings never dominate the grand canonical ensemble. The behaviour of our solutions in the microcanonical ensemble approaches known perturbative results in the thin-ring limit.
Maximally symmetric curved-brane solutions are studied in dilatonic braneworld models which realise the self-tuning of the effective four-dimensional cosmological constant. It is found that no vacua in which the brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the near-boundary asymptotics of the bulk fields. In the holographic dual picture, this corresponds to coupling the UV CFT to a curved metric (possibly with a defect). Alternatively, the same may be achieved in a flat-space QFT with suitable variable scalar sources. With these ingredients, it is found that maximally symmetric, positive and negative curvature solutions with a stabilised brane position generically exist. The space of such solutions is studied in two different types of realisations of the self-tuning framework. In some regimes we observe a large hierarchy between the curvature on the brane and the boundary UV CFT curvature. This is a dynamical effect due to the self-stabilisation mechanism. This setup provides an alternative route to realising de Sitter space in string theory.
Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, $phi^4$ theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS.
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