Max Planck Institute for Physics

A bstract How to turn the flip of a coin into a random variable whose expected value equals a scattering amplitude? We answer this question by constructing a numerical algorithm to evaluate curve integrals — a novel formulation of scattering amplitudes — by a Monte Carlo strategy. To achieve a satisfactory accuracy we take advantage of tropical importance sampling. The crucial result is that the sampling procedure can be realized as a stochastic process on surfaces which can be simulated efficiently on a computer. The key insight is to let go of the Feynman-bias that amplitudes should be presented as a sum over diagrams, and instead re-arrange the sum as suggested by a dual decomposition of curve integrals. We attach an implementation of this algorithm as an ancillary file, which we have used to evaluate amplitudes for the massive Tr( ϕ ) 3 theory in D = 2 space-time dimensions, up to 10-loops. Interestingly, we observe experimentally that the number of sample points required to achieve a fixed accuracy remains significantly smaller than what the number of diagrams would suggest. Finally we propose an extension of our method which is inspired by ideas from artificial intelligence. We use the stochastic process to define a parametrization for a space of distributions, where we formulate importance sampling for an arbitrary curve integrand as a convex optimization problem.

The ongoing Euclid mission aims to measure spectroscopic redshifts for approximately two million galaxies using the H $α$ line emission detected in near-infrared slitless spectroscopic data from the Euclid Deep Fields (EDFs). These measurements will reach a flux limit of $5\times 10^{-17}\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ in the redshift range $0.4<z<1.8$, opening the door to numerous investigations involving galaxy evolution, extending well beyond the mission's core objectives. The achieved H $α$ luminosity depth will lead to a sufficiently high sampling, enabling the reconstruction of the large-scale galaxy environment. We assess the quality of the reconstruction of the galaxy cosmic web environment with the expected spectroscopic dataset in EDFs. The analysis is carried out on the Flagship and GAEA galaxy mock catalogues. The quality of the reconstruction is first evaluated using geometrical and topological statistics measured on the cosmic web, namely the length of filaments, the area of walls, the volume of voids, and its connectivity and multiplicity. We then quantify how accurately gradients in galaxy properties with distance from filaments can be recovered. As expected, the small-scale redshift-space distortions, have a strong impact on filament lengths and connectivity, but can be mitigated by compressing galaxy groups before skeleton extraction. The cosmic web reconstruction is biased when relying solely on H $α$ emitters. This limitation can be mitigated by applying stellar mass weighting during the reconstruction. However, this approach introduces non-trivial biases that need to be accounted for when comparing to theoretical predictions. Redshift uncertainties pose the greatest challenge in recovering the expected dependence of galaxy properties, though the well-established stellar mass transverse gradients towards filaments can still be observed.

A bstract We present a formulation of the three- and four-point amplitudes on the Coulomb branch of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM as integrals over the symplectic Grassmannian. We demonstrate that their kinematic spaces are equivalent to symplectic Grassmannians SpGr( n , 2 n ). For the three-point case, we express the amplitude as an integral over the symplectic Grassmannian in a specific little group frame. In the four-point case, we show that the integral yields the amplitude up to a known kinematic factor. Building on the four-dimensional analysis, we also express the six-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (1, 1) SYM amplitude in terms of four-dimensional variables in a form that makes its symplectic Grassmannian structure manifest.

In this work, we develop a unified framework for Conformal Gravity and Noncommutative (Fuzzy) Gravity incorporating internal interactions. Our approach relies on two fundamental observations: first, the dimensions of a curved manifold and those of its tangent group need not coincide, and second, both gravitational models can be formulated as gauge theories. We begin with a discussion of the gauge-theoretic formulation of gravitational dynamics, emphasizing the role of diffeomorphism invariance. We then outline the constructions of Conformal Gravity and Fuzzy Gravity within this formalism. Building on an extension of the four-dimensional tangent group, we propose a scheme that unifies the two theories while naturally incorporating internal degrees of freedom. We further investigate the low-energy limits that emerge after appropriate spontaneous symmetry-breaking mechanisms, and we comment on potential observational signatures—particularly those associated with cosmic strings and their imprint on gravitational-wave spectra.

Abstract In this article we investigate the property of complete monotonicity within a special family $$\mathcal {F}_s$$ F s of functions in s variables involving logarithms. The main result of this work provides a linear isomorphism between $$\mathcal {F}_s$$ F s and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in $$\mathcal {F}_s$$ F s is semi-algebraic. This gives a finite time algorithm to decide whether a function in $$\mathcal {F}_s$$ F s is completely monotone.

(Abridged) The bimodality between star-forming discs and quiescent spheroids requires the existence of two main processes: the galaxy quenching and the morphological transformation. In this paper, we aim to understand the link between these processes and their relation with the stellar mass of galaxies and their local environment. Taking advantage of the first data released by the Euclid Collaboration, covering more than 60 deg2 with space-based imaging and photometry, we analyse a mass-complete sample of nearly one million galaxies in the range 0.2510^{9.5} M_\odot$. We divide the sample into four sub-populations of galaxies, based on their star-formation activity and morphology. We then analyse the physical properties of these populations and their relative abundances in the stellar mass vs. local density plane. Together with confirming the passivity-density relation and the morphology-density relation, we find that quiescent discy galaxies are more abundant in the low-mass regime of high-density environment. At the same time, star-forming bulge-dominated galaxies are more common in field regions, preferentially at high masses. Building on these results and interpreting them through comparison with simulations, we propose a scenario where the evolution of galaxies in the field significantly differs from that in higher-density environments. The morphological transformation in the majority of field galaxies takes place before the onset of quenching and is mainly driven by secular processes taking place within the main sequence, leading to the formation of star-forming bulge-dominated galaxies as intermediate-stage galaxies. Conversely, quenching of star formation precedes morphological transformation for most galaxies in higher-density environments. This causes the formation of quiescent disc-dominated galaxies before their transition into bulge-dominated ones.

Abstract To give more credence to the M-theoretic Emergence Proposal it is important to show that also classical kinetic terms in a low energy effective action arise as a quantum effect from integrating out light towers of states. We show that for compactifications of type IIA on Calabi-Yau manifolds, the classical weak coupling Yukawa couplings, which are the triple intersection numbers of the Calabi-Yau threefold, can be obtained from the 1/2-BPS protected one-loop Schwinger integral over D2-D0 bound states, after employing a novel regularization for the final infinite sum of Gopakumar-Vafa invariants. Approaching the problem in a consecutive manner from 6D decompactification over emergent string to the ultimate M-theory limits, we arrive at a mathematically concrete regularization that involves finite distance degeneration limits of Calabi-Yau threefolds in an intriguing way. We test and challenge this proposal by the concrete determination of the periods around such degeneration points for threefolds with one Kähler modulus and the two examples ℙ 1, 1, 1, 6, 9[18] and ℙ 1, 1, 2, 2, 6[12].

Abstract We study the recently introduced curve integral formalism that defines a new family of formulas for the scattering amplitudes of the colored scalar trϕ 3 theory. We find that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, n, and the loop order, L, is effectively decoupled in these formulas. We derive the curve integrals at tree-level for all n. We then show that, for higher loop-order, it suffices to study the curve integrals for L-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the tree-level results, we find formulas for the all n amplitudes at L loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all n.

Abstract A search for a pseudoscalar a produced in association with a top-quark pair, or in association with a single top quark plus a W boson, with the pseudoscalar decaying into b -quarks ( $$a\rightarrow b\bar{b}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>→</mml:mo> <mml:mi>b</mml:mi> <mml:mover> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> ), is performed using the full Run 2 data sample using a dileptonic decay mode signature. The search covers pseudoscalar boson masses between 12 and 100 GeV and involves both the kinematic regime where the decay products of the pseudoscalar are reconstructed as two standard b -tagged small-radius jets, or merged into a large-radius jet due to its Lorentz boost. No significant excess relative to expectations is observed. Assuming a branching ratio $$\text {BR}(a\rightarrow b\bar{b})=100\% $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>BR</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>→</mml:mo> <mml:mi>b</mml:mi> <mml:mover> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>100</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> , the range of pseudoscalar masses between 50 and 80 GeV is excluded at 95% confidence level for a coupling of the pseudoscalar to the top quark of 0.5, while a coupling of 1.0 is excluded at 95% confidence level for the masses considered, with the coupling defined as the strength modifier of the Standard Model Yukawa coupling.

This paper presents a highly tunable low-g microelectromechanical systems (MEMS) inertial switch. The switch is specifically designed as a low-power wake-up device for Internet-of-Things (IoT) applications. The designed inertial switch is sensitive to in-plane accelerations in all directions (omnidirectional). The proposed inertial switch has been modeled and simulated both analytically and using finite element analysis techniques. The switch prototype has been fabricated through an in-house optimized silicon-on-insulator (SOI) wafer process, which allows patterning on both the device and handle silicon layers. The fabricated inertial switch was experimentally tested using a closed-loop shaker system to measure acceleration thresholds and a tilt stage for electrical resistance measurements. This inertial switch demonstrates the ability to tune the acceleration threshold in a wide range of 0.25 g to 2 g. This promising inertial sensor holds a significant potential for applications requiring a high dynamic range for acceleration threshold detection, such as mechanical wake-up functions in IoT devices.