Non-expanding horizons: multipoles and the symmetry group

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1–3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group $$ \mathfrak{G} $$ G of NEHs is a 1-dimensional extension of the BMS group $$ \mathfrak{B} $$ B . These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $$ \mathcal{I} $$ I ±of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that $$ \mathcal{I} $$ I ± have a small additional structure that reduces $$ \mathfrak{G} $$ G to the BMS group $$ \mathfrak{B} $$ B , and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $$ \mathcal{I} $$ I +.

Quantum gravity on the black hole horizon

We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in ħ and γ ∼ MPl/MBH. These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, s » γ2$$ {M}_{\mathrm{Pl}}^2 $$ M Pl 2 , for semi-classical black holes. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same.

New Cosmological Solutions of a Nonlocal Gravity Model

A nonlocal gravity model (2) was introduced and considered recently, and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a nonsingular time symmetric bounce. In the present paper, we investigate other possible exact cosmological solutions and find some the new ones in nonflat space. Used nonlocal gravity dynamics can change the background topology. To solve the corresponding equations of motion, we first look for a solution of the eigenvalue problem □(R−4Λ)=q(R−4Λ). We also discuss possible extension of this model with a nonlocal operator, symmetric under □⟷□−1, and its connection with another interesting nonlocal gravity model.

Asymptotic symmetries at null-infinity for the Rarita-Schwinger field with magnetic term

In this paper we study the magnetic charges of the free massless Rarita-Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang-Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

Universe as Klein–Gordon eigenstates

We formulate Friedmann’s equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the$$\beta $$ β -times $$t_\beta :=\int ^t a^{-2\beta }$$ t β : = ∫ t a - 2 β , where a is the scale factor. In particular, it turns out that Friedmann’s equations are equivalent to the eigenvalue problems $$\begin{aligned} O_{1/2} \Psi =\frac{\Lambda }{12}\Psi , \quad O_1 a =-\frac{\Lambda }{3} a , \end{aligned}$$ O 1 / 2 Ψ = Λ 12 Ψ , O 1 a = - Λ 3 a , which is suggestive of a measurement problem. $$O_{\beta }(\rho ,p)$$ O β ( ρ , p ) are space-independent Klein–Gordon operators, depending only on energy density and pressure, and related to the Klein–Gordon Hamilton–Jacobi equations. The $$O_\beta $$ O β ’s are also independent of the spatial curvature, labeled by k, and absorbed in $$\begin{aligned} \Psi =\sqrt{a} e^{\frac{i}{2}\sqrt{k}\eta } . \end{aligned}$$ Ψ = a e i 2 k η . The above pair of equations is the unique possible linear form of Friedmann’s equations unless $$k=0$$ k = 0 , in which case there are infinitely many pairs of linear equations. Such a uniqueness just selects the conformal time $$\eta \equiv t_{1/2}$$ η ≡ t 1 / 2 among the $$t_\beta $$ t β ’s, which is the key to absorb the curvature term. An immediate consequence of the linear form is that it reveals a new symmetry of Friedmann’s equations in flat space.

Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space

Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.

Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

Relation between parity-even and parity-odd CFT correlation functions in three dimensions

In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as $$ {\mathcal{W}}^3 $$ W 3 and $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ W 2 W ˜ . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

Towards bootstrapping RG flows: sine-Gordon in AdS

The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.