We derived in arXiv:2206.04188 arXiv:2211.15712 a compact expression for the $N$-th rank QED polarization tensor $Π_{μ_1\cdots μ_N}(k_1,\cdots,k_N)$ in a $(0+1)$-dimensional worldline framework. This fully off-shell object, a function of $N$ external photon four-momenta, is a key ingredient in high-order computations of cusp anomalous dimensions and lepton anomalous magnetic moments. We demonstrate here that $Π_{μ_1\cdots μ_N}$ can further be expressed simply in terms of a small number of independent ``head" form factors (each representing $(N-1)!/2$ Feynman diagrams) which have a universal structure in terms of sums over fermion Green functions and (propertime derivative of) their boson worldline superpartners. This worldline representation bypasses explicit Wick contractions and avoids tensor reductions to scalar loop integrals à la Passarino and Veltman, order by order in perturbation theory. We give explicit expressions for the $4$-th and $6$-th rank head form factors and provide a computer script generalizing these results to arbitrary $N$ external photons. The multiplicity of heads, and their growth with $N$, can be understood in terms of orbits of the permutation group. We employ the Burnside-Cauchy-Frobenius lemma to show that it scales as $e^{N-1}/\sqrt{N}$ terms as opposed to the $e^{N-1} N!/\sqrt{N}$ terms in conventional perturbation theory. We reexpress worldline parameter integrals that define the $4$-th rank heads as Feynman parameter integrals to reproduce the seminal results by Karplus and Neuman for the on-shell light-by-light amplitude and extend these to the fully off-shell case in massless QED employing a tailored integration-by-parts procedure. In a follow-up paper, we will discuss the direct computation of worldline integrals, potentially providing a further $N!$ advantage relative to Feynman diagram computations at high orders in perturbation theory.
The shortcomings of the Standard Model (SM) motivate its extension to accommodate new expected phenomena, such as dark matter and neutrino masses. However, such extensions are generally more complex due to the presence of a large number of free parameters and additional phenomenology. Understanding how theoretical and experimental limits affect the parameter spaces of new models, individually and collectively, is of utmost importance for conducting model status analysis, motivating precise computations, or model-building aimed at solving certain issues. However, checking the constraints usually require a large amount of time using a chain of physics tools. We demonstrate, for the first time, the application of deep learning (DL) for the multilabel classification (MLC) of a group of theoretical and experimental constraints in the dark doublet phase of the next-to-two-Higgs-doublet model (DDP-N2HDM), as a representative 9-dimensional parameter space. We analyze the issue of class imbalance and the ability of the classifier to learn joint class distributions. We demonstrate the time advantage compared to physics tools, with the classifier achieving orders of magnitude faster checks on groups of constraints and strong performance. The classifier performed strongly in terms of identifying regions where all constraints are valid or invalid, as well as regions where one or more of the constraints are valid or invalid simultaneously. This approach can be applied to any extension beyond the SM with the potential to aid HEP tools or act as a surrogate for fast model status checks. To that end, we provide a python tool \texttt{HEPMLC} for generating and investigating multilabel classifiers for SM extensions.
We find all polynomial tau-functions of the n-th reduced BKP hierarchy (=n-th Sawada-Kotera hierarchy). The name comes from the fact that for n=3 the simplest equation of the hierarchy is the famous Sawada-Kotera equation.
By using the approach introduced in Ganchev et al. (Q-Balls Meet Fuzzballs: Non-BPS Microstate Geometries. arXiv:2107.09677 [hep-th]) we construct non-BPS solutions of 6D (1, 0) supergravity coupled to two tensor multiplets as a perturbation of AdS3×S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {AdS}_3\times S^3$$\end{document}. These solutions are both regular and asymptotically AdS3×S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {AdS}_3\times S^3$$\end{document}, so according to the standard holographic framework they must have a dual CFT interpretation as non-supersymmetric heavy operators of the D1–D5 CFT. We provide quantitative evidence that such heavy CFT operators are bound states of a large number of light BPS operators that are mutually non-BPS.
We investigate bounce cosmological models in the presence of a viscous fluid, making use of generalized holographic cutoffs introduced by Nojiri and Odintsov [Covariant generalized holographic dark energy and accelerated universe, Eur. Phys. J. C 77 (2017) 528, arXiv:1703.06372 [hep-th]]. We consider both an exponential, a power-law, and a double exponential form for the scale factor. By use of these models, we calculate expressions for infrared cutoffs analytically, such that they correspond to the particle horizon at the bounce. Finally, we derive the energy conservation equation, from the holographic point of view. In that way, the relationship between the viscous fluid bounce and the holographic bounce is demonstrated.