We calculate the central charges a, c and k G of a large class of fourdimensional N = 2 superconformal field theories arising from compactifying the sixdimensional N = (2, 0) theory on a Riemann surface with regular and irregular punctures. We also study the renormalization group flows between the general Argyres-Douglas theories, which all agree with the a-theorem.

We interpret certain Seiberg-like dualities of two-dimensional N =(2, 2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kähler moduli space of manifolds constructed from the corresponding Kähler quotients. We study the S 2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor whose physical origin and consequences we spell out in detail. We also present similar dualities in N =(2, 2) * quiver gauge theories, which are related to dualities of quantum integrable spin chains.

Contamination by heavy metals is a significant issue worldwide. In recent decades, soil heavy metals pollutants in China had adverse impacts on soil quality and threatened food security and human health. Anthropogenic inputs mainly generate heavy metal contamination in China. In this review, the approaches were used in these investigations, focusing on geochemical strategies and metal isotope methods, particularly useful for determining the pathway of mining and smelting derived pollution in the soil. Our findings indicate that heavy metal distribution substantially impacts topsoils around mining and smelting sites, which release massive amounts of heavy metals into the environment. Furthermore, heavy metal contamination and related hazards posed by Pb, Cd, As, and Hg are more severe to plants, soil organisms, and humans. It’s worth observing that kids are particularly vulnerable to Pb toxicity. And this review also provides novel approaches to control and reduce the impacts of heavy metal pollution. Hydrometallurgy offers a potential method for extracting metals and removing potentially harmful heavy metals from waste to reduce pollution. However, environmentally friendly remediation of contaminated sites is a significant challenge. This paper also evaluates current technological advancements in the remediation of polluted soil, such as stabilization/solidification, natural attenuation, electrokinetic remediation, soil washing, and phytoremediation. The ability of biological approaches, especially phytoremediation, is cost-effective and favorable to the environment.