Annales Henri Poincaré最新文献

The precise renormalizable interactions in the bosonic sector of electroweak theory are intrinsically determined in the autonomous approach to perturbation theory. This proceeds directly on the Hilbert–Fock space built on the Wigner unirreps of the physical particles, with their given masses: those of three massive vector bosons, a photon, and a massive scalar (the “higgs”). Neither “gauge choices” nor an unobservable “mechanism of spontaneous symmetry breaking” is invoked. Instead, to proceed on Hilbert space requires using string-localized fields to describe the vector bosons. In such a framework, the condition of string independence of the ({mathbb {S}})-matrix yields consistency constraints on the coupling coefficients, the essentially unique outcome being the experimentally known one. The analysis can be largely carried out for other configurations of massive and massless vector bosons, paving the way towards consideration of consistent mass patterns beyond those of the electroweak theory.

We study the inverse problem of recovering primordial perturbations from anisotropies of the cosmic microwave background (CMB) using the kinetic model. Mathematically, the problem in concern is the inverse source problem for the linear Boltzmann equation with measurements on some Cauchy surface. We obtain two stable determination results for generic absorption coefficients and scattering kernels.

We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of the latter tensorized with a real free fermion VOSA. Furthermore, excluding the ones with central charge 24 of glueing type III and with no real free fermion, we show that they are all strongly graded-local. In particular, they naturally give rise to holomorphic graded-local conformal nets. In total, we are able to prove that 910 of the 969 nice holomorphic VOSAs with central charge 24 and with non-trivial odd part are strongly graded-local, without counting hypothetical fake copies of the shorter moonshine VOSA tensorized with a real free fermion VOSA.

We propose a geometric characterisation of the topological string partition functions associated with the local Calabi–Yau (CY) manifolds used in the geometric engineering of (d=4), ({mathcal {N}}=2) supersymmetric field theories of class ({mathcal {S}}). A quantisation of these CY manifolds defines differential operators called quantum curves. The partition functions are extracted from the isomonodromic tau-functions associated with the quantum curves by expansions of generalised theta series type. It turns out that the partition functions are in one-to-one correspondence with preferred coordinates on the moduli spaces of quantum curves defined using the Exact WKB method. The coordinates defined in this way jump across certain loci in the moduli space. The changes of normalization of the tau-functions associated with these jumps define a natural line bundle playing a key role in the geometric characterisation of the topological string partition functions proposed here.

In the perturbative treatment of interacting quantum field theories, if the interaction Lagrangian changes adiabatically in a finite interval of time, secular growths may appear in the truncated perturbative series also when the interaction Lagrangian density is returned to be constant. If this happens, the perturbative approach does not furnish reliable results in the evaluation of scattering amplitudes or expectation values. In this paper we show that these effects can be avoided for adiabatically switched-on interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. We start considering equilibrium background states and show that, when thermalisation occurs (interaction Lagrangian of spatial compact support), secular effects are avoided. Furthermore, no secular effects pop up if the limit where the Lagrangian is supported everywhere in space is taken after thermalisation (large time limit), in contrast to the reversed order. This result is generalized showing that if the interaction Lagrangian is spatially compact, secular growths are avoided for generic background states which are only invariant under time translation and to states whose explicit dependence of time is not too strong. Finally, as an application, the presented theorems are used to study a complex scalar and a Dirac field, on a background KMS state, in a classical external electromagnetic potential and the contribution to the two point-function given by a generic loop diagram arising from a second order perturbative expansion.

Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calderón projectors for the Wick-rotated equations induce Hadamard bi-solutions on the Lorentzian level. On the other hand, we find smoothing obstructions to gauge-invariance and positivity conditions needed in quantization. These obstructions are primarily due to boundary terms arising in the Wick-rotated theory and depend on the boundary conditions.

We study the time evolution of single-particle quantum states described by a Lindblad master equation with local terms. By means of a geometric resolvent equation derived for Lindblad generators, we establish a finite-volume-type criterion for the decay of the off-diagonal matrix elements in the position basis of the time-evolved or steady states. This criterion is shown to yield exponential decay for systems where the non-hermitian evolution is either gapped or strongly disordered. The gap exists, for example, whenever any level of local dephasing is present in the system. The result in the disordered case can be viewed as an extension of Anderson localization to open quantum systems.

The general classification of (3+1)-static black hole solutions of the Einstein equations, with or without matter, is central in general relativity and important in geometry. In the realm of (textrm{S}^{1})-symmetric vacuum spacetimes, a recent classification proved that, without restrictions on the topology or the asymptotic behavior, black hole solutions can be only of three kinds: (i) Schwarzschild black holes, (ii) Boost black holes or (iii) Myers–Korotkin–Nicolai black holes, each one having its distinct asymptotic and topological type. In contrast to this, very little is known about the general classification of (textrm{S}^{1})-symmetric static electrovacuum black holes although examples show that, on the large picture, there should be striking differences with respect to the vacuum case. A basic question then is whether or not there are charged analogs to the static vacuum black holes of types (i), (ii) and (iii). In this article, we prove the remarkable fact that, while one can ‘charge’ the Schwarzschild solution (resulting in a Reissner–Nordström spacetime) preserving the asymptotic, one cannot do the same to the Boosts and to the Myers–Korotkin–Nicolai solutions: The addition of a small or large electric charge, if possible at all, would transform entirely their asymptotic behavior. In particular, such vacuum solutions cannot be electromagnetically perturbed. The results of this paper are consistent but go far beyond the works of Karlovini and Von Unge on periodic analogs of the Reissner–Nordström black holes. The type of result as well as the techniques used is based on comparison geometry a la Bakry–Émery and appears to be entirely novel in this context. The findings point to a complex interplay between asymptotic, topology and charge in spacetime dimension (3+1), markedly different from what occurs in higher dimensions.

In this paper, we study the long-time dynamics of solutions to the defocusing semilinear wave equation (Box _gphi =|phi |^{p-1}phi ) on the Schwarzschild black hole spacetimes. For (frac{1+sqrt{17}}{2}<p<5) and compactly supported initial data, we show that the solution decays like (|phi |lesssim t^{-1+epsilon }) in the domain of outer communication. The proof relies on the r-weighted vector field method of Dafermos–Rodnianski together with the Strichartz estimates for linear waves by Marzuola–Metcalfe–Tataru–Tohaneanu.

In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation governs the flow of the effective average action, under changes of a mass parameter k. Here we introduce an analogous flow equation for gauge theories, with the aid of the Batalin–Vilkovisky (BV) formalism. We also show that the corresponding effective average action satisfies a Slavnov–Taylor identity in Zinn-Justin form. We interpret the equation as a cohomological constraint on the functional form of the effective average action, and we show that it is consistent with the flow.