Curious Aspects of Three-Dimensional N=1{\cal N}=1 SCFTs

We study the dynamics of certain 3d ${\cal N}=1$ time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared and there exists (nonetheless) an exact moduli space of vacua. This theory has a dual description with manifest time reversal symmetry. Second, we consider some surprising facts about ${\cal N}=2$ $U(1)$ gauge theory coupled to two chiral superfields of charge 1. This theory is claimed to have emergent $SU(3)$ global symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a theory of scalars and fermions but no gauge fields) with manifest $SU(3)$ symmetry but only ${\cal N}=1$ supersymmetry. We argue that this Wess-Zumino model must have enhanced supersymmetry in the infrared. Finally, we make some brief comments about the dynamics of ${\cal N}=1$ $SU(N)$ gauge theory coupled to $N_f$ quarks in a time reversal invariant fashion. We argue that for $N_f<N$ there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted.Comment: 30 pages, 4 figures v2: references adde

Quantum cluster approach to the spinful Haldane-Hubbard model

We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial N\'eel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial N\'eel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.Comment: 11 pages, 12 figures. Published versio

Variational Thermal Quantum Simulation via Thermofield Double States

We present a variational approach for quantum simulators to realize finite temperature Gibbs states by preparing thermofield double (TFD) states. Our protocol is motivated by the quantum approximate optimization algorithm (QAOA) and involves alternating time evolution between the Hamiltonian of interest and interactions which entangle the system and its auxiliary counterpart. As a simple example, we demonstrate that thermal states of the 1d classical Ising model at any temperature can be prepared with perfect fidelity using L/2 iterations, where L is system size. We also show that a free fermion TFD can be prepared with nearly optimal efficiency. Given the simplicity and efficiency of the protocol, our approach enables near-term quantum platforms to access finite temperature phenomena via preparation of thermofield double states.Comment: 5 + 2 pages, 5 figure

Defects and Boundaries in Quantum Field Theories

We discuss some aspects of defects and boundaries in quantum field theories (QFTs) and their applications in revealing non-perturbative aspects of QFTs in combination with other techniques, including integrability. Firstly, we study the Kondo line defects that arise from local impurities chirally coupled to a two-dimensional conformal field theory. They have interesting defect Renormalization Group flows and integrability properties. We give a construction from four-dimensional Chern Simons theory whose two-dimensional compactification leads to a 2d CFT with Kondo line insertion. This construction will provide new perspectives into the surprising integrable properties of Kondo line defects. Secondly, we study the ODE/IM correspondence, which states a surprising link between conformal field theories and the spectral problems of ordinary differential equations. A direct derivation of the correspondence is still unknown. We study a more refined description by directly relating the expectation values of a Kondo defect line and the generalized monodromy data of an ODE. Thanks to the 4d Chern Simons construction, we conjecture an explicit recipe for constructing the ODE corresponding to a Kondo defect. New examples we discuss include the isotropic/anisotropic Kondo defects in the multichannel $\prod_i SU(2)_{k_i}$ WZW models. We then extend the ODE/IM correspondence we find to the excited states, which provides a full solution to the spectral problems for the affine Gaudin model and the Kondo defects. In particular, by generalizing and applying techniques of exact WKB analysis, we derive the non-perturbative infra-red behaviours and wall-crossing properties of a large class of Kondo line defects. Finally, we study the conformal boundary conditions of a four-dimensional Abelian gauge field. One starts by coupling a three-dimensional CFT with a $U(1)$ symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrised by the gauge coupling $\tau$ in the upper-half plane and by the choice of the 3d CFT in the decoupling limit $\tau \to \infty$. The $SL(2,\mathbb{Z})$ electromagnetic transformations act on the BCFTs and relate different 3d CFTs in the various decoupling limits. We study the general properties of this BCFT and show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. We propose a new computational scheme that can be used to approximate observables in strongly coupled 3d CFTs. As an example, we consider the 3d CFT to be one Dirac fermion and compute scaling dimensions of various boundary operators and the hemisphere free-energy up to two loops. Using an $S$-duality improved ansatz, we extrapolate the perturbative results and find good approximations to the observables of the $O(2)$ model

Universal Non-Invertible Symmetries

It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a d-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d-1)-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this (d-1)-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a (d-1)-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on (d-3)-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.Comment: 75 pages. v2: Minor improvement

Assessment of multi-air emissions: case of particulate matter (dust), SO2, NOx and CO2 from iron and steel industry of China

Industrial activities are generally energy and air emissions intensive, requiring bulky inputs of raw materials and fossil fuels and emitting huge waste gases including particulate matter (PM, or dust), sulphur dioxide (SO2), nitrogen oxides (NOx), carbon dioxide (CO2), and other substances, which are severely damaging the environment. Many studies have been carried out on the quantification of the concentrations of these air emissions. Although there are studies published on the co-effect of multi-air emissions, a more fair and comprehensive method for assessing the environmental impact of multi-air emissions is still lacking, which can simultaneously consider the flow rate of waste gases, the availability of emitting sources and the concentrations of all emission substances. In this work, a Total Environmental Impact Score (TEIS) approach is proposed to assess the environmental impact of the main industrial processes of an integrated iron and steel site located in the northeast of China. Besides the concentration of each air emission substance, this TEIS approach also combines the flow rate of waste gases and the availability of emitting sources. It is shown that the processes in descending order by the values of TEIS are sintering, ironmaking, steelmaking, thermal power, steel rolling, and coking, with the values of 17.57, 16.68, 10.86, 10.43, 9.60 and 9.27, respectively. In addition, a sensitivity analysis was conducted, indicating that the TEIS order is almost the same with the variation of 10% in the permissible CO2 concentration limit and the weight of each air emission substance. The effects of emitting source availability and waste gas flow rate on the TEIS cannot be neglected in the environmental impact assessment

On 18\frac18-BPS black holes and the chiral algebra of N=4\mathcal{N}=4 SYM

We investigate the existence of $\frac18$-BPS black hole microstates in Type IIB string theory on $\mathrm{AdS}_5 \times \mathrm{S}^5$. As will be explained, these states are in one-to-one correspondence with the Schur operators comprising the chiral algebra of $\mathcal{N}=4$ super-Yang-Mills, and a conjecture of Beem et al. implies that the Schur sector only contains graviton operators and hence $\frac18$-BPS black holes do not exist. We scrutinize this conjecture from multiple angles. Concerning the macroscopic counting, we rigorously prove that the flavored Schur index cannot exhibit black hole entropy growth, and provide numerical evidence that the flavored MacDonald index also does not exhibit such growth. Next, we go beyond counting to examine the algebraic structure, beginning by presenting evidence for the well-definedness of the super-$\mathcal{W}$ algebra of Beem et al., then using modular differential equations to argue for an upper bound on the lightest non-graviton operator if existent, and finally performing a systematic construction of cohomologies to recover only gravitons. Along the way, we clarify key aspects of the 4d/2d correspondence using the formalism of the holomorphic topological twist.Comment: 36+15 pages, 5 figures, 6 table

A novel statistical method for long-term coronavirus modelling

Background: Novel coronavirus disease has been recently a concern for worldwide public health. To determine epidemic rate probability at any time in any region of interest, one needs efficient bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of novel coronavirus infection rate. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the multi-dimensionality advantage, that suggested methodology offers, namely dealing efficiently with multiple regions at the same time and accounting for cross-correlations between different regional observations. Methods: Modern multi-dimensional novel statistical method was directly applied to raw clinical data, able to deal with territorial mapping. Novel reliability method based on statistical extreme value theory has been suggested to deal with challenging epidemic forecast. Authors used MATLAB optimization software. Results: This paper described a novel bio-system reliability approach, particularly suitable for multi-country environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of extreme novel coronavirus death rate probability. Namely, accurate maximum recorded patient numbers are predicted for the years to come for the analyzed provinces. Conclusions: The suggested method performed well by supplying not only an estimate but 95% confidence interval as well. Note that suggested methodology is not limited to any specific epidemics or any specific terrain, namely its truly general. The only assumption and limitation is bio-system stationarity, alternatively trend analysis should be performed first. The suggested methodology can be used in various public health applications, based on their clinical survey data.publishedVersio

Oil tanker under ice loadings

As a result of global warming, the area of the polar pack ice is diminishing, making merchant travel more practical. Even if Arctic ice thickness reduced in the summer, fractured ice is still presenting operational risks to the future navigation. The intricate process of ship-ice interaction includes stochastic ice loading on the vessel hull. In order to properly construct a vessel, the severe bow forces that arise must be accurately anticipated using statistical extrapolation techniques. This study examines the severe bow forces that an oil tanker encounters when sailing in the Arctic Ocean. Two stages are taken in the analysis. Then, using the FEM program ANSYS/LS-DYNA, the oil tanker bow force distribution is estimated. Second, in order to estimate the bow force levels connected with extended return periods, the average conditional exceedance rate approach is used to anticipate severe bow forces. The vessel’s itinerary was planned to take advantage of the weaker ice. As a result, the Arctic Ocean passage took a meandering route rather than a linear one. As a result, the ship route data that was investigated was inaccurate with regard to the ice thickness data encountered by a vessel yet skewed with regard to the ice thickness distribution in the region. This research intends to demonstrate the effective application of an exact reliability approach to an oil tanker with severe bow forces on a particular route.publishedVersio