Higher-order QCD corrections to H → b$$ \overline{b} $$ from rational approximants

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to Γ(H → b$$ \overline{b} $$ b ¯ ), to be c5 = −6900 ± 1400. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → b$$ \overline{b} $$ b ¯ ) will remain largely dominated by the Standard Model parameters.

Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors

In this paper, we discuss the effects of nonlinear electrodynamics (NED) on non-rotating black holes, parametrized by the field coupling parameter β and magnetic charge parameter P in detail. Particularly, we survey a large range of observables and physical properties of the magnetically charged black hole, including the thermodynamic properties, observational appearance, quasinormal modes and absorption cross sections. Initially, we show that the NED black hole is always surrounded by an event horizon and any magnetic charge is permissible. We then show that the black hole gets colder with increasing charge. Investigating the heat capacity, we see that the black hole is thermally stable between points of phase transition. Introducing a generalized uncertainty principle (GUP) with a quantum gravity parameter λ extends the range of the stable region, but the effect on temperature is negligible. Then we compute the deflection angle at the weak field limit, by the Gauss-Bonnet theorem and the geodesic equation, and find that even at the first order, the magnetic charge has a contribution due to the “field mass” term. Small changes of the charge contributes greatly to the paths of null geodesics due to the P 2 dependence of the horizon radius. Using a ray-tracing code, we simulate the observational appearance of a NED black hole under different emission profiles, thin disk and spherical accretion. We find that the parameter P has a very strong effect on the observed shadow radius, in agreement with the deflection angle calculations. We finally consider quasinormal modes under massless scalar perturbations of the black hole and the greybody factor. We find that the charge introduces a slight difference in the fundamental frequency of the emitted waveform. We find that the greybody factor of the NED black hole is strongly steepened by the introduction of increasing charge. To present observational constrains, we show that the magnetic charge of the M87* black hole is between 0 ≤ P ≤ 0.024 in units of M, in agreement with the idea that real astrophysical black holes are mostly neutral. We also find that LIGO/VIRGO and LISA could detect NED black hole perturbations from BHs with masses between 5 M ☉ and 8.0 · 108 M ☉. We finally show that for black holes with masses detected with LIGO so far, charged NED black holes would deviate from Schwarzschild by 5∼10 Hz in their fundamental frequencies.

Static solutions in the Freund – Nambu scalar-tensor theory of gravitation

Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

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.

Absorption by stringy black holes

We investigate the absorption of planar massless scalar waves by a charged rotating stringy black hole, namely a Kerr–Sen black hole. We compute numerically the absorption cross section and compare our results with those of the Kerr–Newman black hole, a classical general relativity solution. In order to better compare both charged black holes, we define the ratio of the black hole charge to the extreme charge as Q. We conclude that Kerr–Sen and Kerr–Newman black holes have a similar absorption cross section, with the difference increasing for higher values of Q.

The time traveler’s guide to the quantization of zero modes

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder.

Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

An infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann–Lemaître–Robertson–Walker spacetime

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaître–Robertson–Walker spacetimes. For the case of accelerated expansion, we show that the blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

Renormalization and non-renormalization of scalar EFTs at higher orders

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a ‘non-renormalization’ rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing n- and (n− 2)-field operators, with n the maximal number of fields at a fixed mass dimension. The first appears only when the (n− 2)-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.