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A local classification of semisimple algebras of vector fields on $\mathbb{C}^{3}$ is given, using the canonical forms of the Heisenberg algebra and of $sl(2,\mathbb{C})\times sl(2,\mathbb{C})$.

Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at $T=470~$MeV ($\sim 1.5\, T_c$), as well as in 2+1 flavor QCD at $T=220~$MeV ($\sim 1.2 \, T_{pc}$) with $m_{\pi}=320$ MeV. In order to quantify the non-perturbative effects, the lattice correlator is compared with the corresponding $\text{NLO}+\text{LPM}^{\text{LO}}$ estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian Process regression. We find that the resulting photon rates agree within errors., Comment: 20 pages, 16 figures

The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates to existing software. These challenges have to be balanced against constantly changing personnel. At the same time, there is a wide range of applications for HISQ fermions in QCD studies. This situation encourages the development of software featuring a HISQ action that is flexible, high-performing, open source, easy to use, and easy to adapt. In this technical paper, we explain the design strategy, provide implementation details, list available algorithms and modules, and show key performance indicators for SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. The code is publicly available on GitHub., Comment: 17 pages, 7 figures

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using $N_f=2+1$ flavors Highly Improved Staggered Quark (HISQ) action with physical strange quark mass $m_s$, and slightly heavy degenerate up and down quark masses $m_l=m_s/5$ that corresponds to $m_\pi\simeq 320$ MeV. Our results obtained at $T=220$ MeV and $T=251$ MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persist., Comment: 13 pages, 4 figures, Contribution to a special issue of Few Body Systems: Emergence and Structure of Baryons - Selected Contributions from the International Conference Baryons 2022

We extend our analysis of bound states in $\mathcal{N}=1$ supersymmetric Yang-Mills theory by the consideration of baryonic operators, which are composed of three gluino fields. The corresponding states are similar to the baryons in QCD, but due to the difference between gluino and quark fields, their properties and the fermion line contractions involved in their correlation functions are different from QCD. In this work, we first explain the derivation of these operators and the contractions needed in numerical calculations of their correlators. In contrast to QCD the correlators contain a spectacle piece, which requires methods for all-to-all propagators. We provide a first estimate of the two-point function and the mass of the lightest baryonic state in $\mathcal{N}=1$ supersymmetric Yang-Mills theory.

We present charmonium and bottomonium correlators and corresponding reconstructed spectral functions from full QCD calculations in the pseudoscalar channel. Correlators are obtained using a mixed-action approach, clover-improved Wilson valence quarks on gauge field configurations generated with $N_f=2+1$ HISQ sea quarks, with physical strange quark masses and light quark masses corresponding to $m_\pi=315$ MeV. The charm and bottom quark masses are tuned to reproduce the experimental mass spectrum of the spin averaged quarkonium vector mesons from the particle data group. For the spectral reconstruction, we use models based on perturbative spectral functions from different frequency regions like resummed thermal contributions around the threshold from pNRQCD and vacuum contributions well above the threshold. We show preliminary results of the reconstructed spectral function obtained for the first time in our study for full QCD.

Thermal photons from the QGP provide important information about the interaction among plasma constituents. The photon production rate from a thermally equilibrated system is proportional to the transverse spectral function $\rho_T(\omega=|\vec k|, \vec k)$. One can also calculate the photon production rate from the difference between $\rho_T(\omega,\vec k)$ (transverse) and $\rho_L(\omega,\vec k)$ (longitudinal) projections, as $\rho_L$ vanishes on the photon point. Because the UV part of $\rho_T-\rho_L$ is suppressed, the corresponding Euclidean correlator receives most of its contribution from the IR part. We calculate the $T\!-\!L$ correlator on $N_f=2+1$ flavour HISQ configurations with $m_l=m_s/5$ at temperature of about $1.15\,T_{pc}$ (220 MeV). We have used two ans\"{a}tze for the spectral function: 1) A polynomial connected to the UV region consistent with OPE expansion and 2) a hydro-inspired spectral function. We have also applied the Backus-Gilbert method to estimate the spectral function. All these different approaches are combined to estimate the photon production rate., Comment: 10 pages, 7 figures, Contribution to the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany

Single photon emitters in two-dimensional (2D) hexagonal boron nitride (hBN) are promising solid-state quantum emitters for photonic applications and quantum networks. Despite their favorable properties, it has so far remained elusive to determine the origin of these emitters. We focus on two different kinds of hBN samples that particularly lend themselves for integration with nanophotonic devices, multilayer nanoflakes produced by liquid phase exfoliation (LPE) and a layer engineered sample from hBN grown by chemical vapour deposition (CVD). We investigate their inherent defects and fit their emission properties to computationally simulated optical properties of likely carbon-related defects. Thereby we are able to narrow down the origin of emitters found in these samples and find that the C2CB defect fits our spectral data best. In addition, we demonstrate a scalable way of coupling LPE hBN to optical nanofibers that are directly connected to optical fibers. Our work brings us one step closer to specifying the origin of hBN's promising quantum emitters and sheds more light onto the characteristics of emitters in samples that are particularly suited for integration with nanophotonics. This knowledge will prove invaluable for novel nanophotonic platforms and may contribute towards the employment of hBN for future quantum technologies.

Light-matter interactions of defects in two dimensional materials are expected to be profoundly impacted by strong coupling to phonons. In this work, we combine ab initio calculations of a defect in hBN, with a fully quantum mechanical and numerically exact description of a cavity-defect system to elucidate this impact. We show that even at weak light-matter coupling, the dynamical evolution of the cavity-defect system has clear signatures of non-markovian phonon effects, and that linear absorption spectra show the emergence of hybridised light-matter-phonon states in regimes of strong light-matter coupling. We emphasise that our methodology is general, and can be applied to a wide variety of material/defect systems., Comment: 7 pages, 3 figures + 8 pages supplement

A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra., Comment: Final version