A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Importance of charge self-consistency in first-principles description of strongly correlated systems

First-principles approaches have been successful in solving many-body Hamiltonians for real materials to an extent when correlations are weak or moderate. As the electronic correlations become stronger often embedding methods based on first-principles approaches are used to better treat the correlations by solving a suitably chosen many-body Hamiltonian with a higher level theory. The success of such embedding theories, often referred to as second-principles, is commonly measured by the quality of self-energy Σ which is either a function of energy or momentum or both. However, Σ should, in principle, also modify the electronic eigenfunctions and thus change the real space charge distribution. While such practices are not prevalent, some works that use embedding techniques do take into account these effects. In such cases, choice of partitioning, of the parameters defining the correlated Hamiltonian, of double-counting corrections, and the adequacy of low-level Hamiltonian hosting the correlated subspace hinder a systematic and unambiguous understanding of such effects. Further, for a large variety of correlated systems, strong correlations are largely confined to the charge sector. Then an adequate nonlocal low-order theory is important, and the high-order local correlations embedding contributes become redundant. Here we study the impact of charge self-consistency within two example cases, TiSe2 and CrBr3, and show how real space charge re-distribution due to correlation effects taken into account within a first-principles Green’s function-based many-body perturbative approach is key in driving qualitative changes to the final electronic structure of these materials.

Boomerang webs up to three-loop order

Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider the particular class of boomerang webs, consisting of multiple gluon exchanges, but where at least one gluon has both of its endpoints on the same Wilson line. First, we use the replica trick to prove that diagrams involving self-energy insertions along the Wilson line do not contribute to the web, i.e. their exponentiated colour factor vanishes. Consequently boomerang webs effectively involve only integrals where boomerang gluons straddle one or more gluons that connect to other Wilson lines. Next we classify and calculate all boomerang webs involving semi-infinite non-lightlike Wilson lines up to three-loop order, including a detailed discussion of how to regulate and renormalize them. Furthermore, we show that they can be written using a basis of specific harmonic polylogarithms, that has been conjectured to be sufficient for expressing all multiple gluon exchange webs. However, boomerang webs differ from other gluon-exchange webs by featuring a lower and non-uniform transcendental weight. We cross-check our results by showing how certain boomerang webs can be determined by the so-called collinear reduction of previously calculated webs. Our results are a necessary ingredient of the soft anomalous dimension for non-lightlike Wilson lines at three loops.

Cosmic censorship, massless fermionic test fields, and absorption probabilities

In the conventional approach, fermionic test fields lead to a generic overspinning of black holes resulting in the formation of naked singularities. The absorption of the fermionic test fields with arbitrarily low frequencies is allowed for which the contribution to the angular momentum parameter of the space-time diverges. Recently we have suggested a more subtle treatment of the problem considering the fact that only the fraction of the test fields that is absorbed by the black hole contributes to the space-time parameters. Here, we re-consider the interaction of massless spin (1/2) fields with Kerr and Kerr–Newman black holes, adapting this new approach. We show that the drastic divergence problem disappears when one incorporates the absorption probabilities. Still, there exists a range of parameters for the test fields that can lead to overspinning. We employ backreaction effects due to the self-energy of the test fields which fixes the overspinning problem for fields with relatively large amplitudes, and renders it non-generic for smaller amplitudes. This non-generic overspinning appears likely to be fixed by alternative semi-classical and quantum effects.

Worldline description of a bi-adjoint scalar and the zeroth copy

Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show how a global G × $$ \overset{\sim }{G} $$ G ~ symmetry group may be realized by worldline degrees of freedom. The worldline action gives rise to vertex operators, which are compared to similar ones describing the coupling to gauge fields and gravity, thus exposing the color/kinematics interplay in this framework. The action is quantized by path integrals to find a worldline representation of the one-loop QFT effective action of the bi-adjoint scalar cubic theory. As simple applications, we recover the one-loop beta function of the theory in six dimensions, verifying its vanishing, and compute the self-energy correction to the propagator. The model is easily extendable to that of a particle carrying an arbitrary representation of direct products of global symmetry groups, including the multi-adjoint particle, whose one-loop beta function we reproduce as well.

Generalized quantum electrodynamics: One-loop correction

In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in (3[Formula: see text]+[Formula: see text]1) dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag’s theorem undermines the perturbative characterization of the interaction picture due to its inconsistency on quantum field theory foundations. To circumvent this problem, we develop our perturbative approach in the Heisenberg picture and use it to investigate the behavior of the operator current at one-loop. We find the two- and three-point correlation functions are ultraviolet finite, electron self-energy and vertex corrections, respectively. On the other hand, we also explain how the vacuum polarization remains ultraviolet divergent only at [Formula: see text] order. Finally, we evaluate the anomalous magnetic moment, which allows us to specify a lower bound value for the Podolsky parameter.