Conformal symmetry relates the metric on AdS₂ × S¹ to that of S³. This implies that under a suitable choice of boundary conditions for fields on AdS₂ the partition function of conformal field theories on these spaces must agree which makes AdS₂ × S¹ a good testing ground to study localization on non-compact spaces. We study supersymmetry on AdS₂ × S¹ and determine the localizing Lagrangian for \( \mathcal{N} \) = 2 supersymmetric Chern-Simons theory on AdS₂ × S¹. We evaluate the partition function of \( \mathcal{N} \) = 2 supersymmetric Chern-Simons theory on AdS₂ × S¹ using localization, where the radius of S¹ is q times that of AdS₂. With boundary conditions on AdS₂ × S¹ which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS₂, the result for the partition function precisely agrees with that of the theory on the q-fold covering of S³.

We study ${\cal F}^4$-threshold corrections in an eight dimensional S-dual pair of string theories, as a prototype of dual string vacua with sixteen supercharges. We show that the orbifold CFT description of D-string instantons gives rise to a perturbative expansion similar to the one appearing on the fundamental string side. By an explicit calculation, using the Nambu-Goto action in the static gauge, we show that the first subleading term agrees precisely on the two sides. We then give a general argument to show that the agreement extends to all orders.

Energy efficiency potentially reduces global carbon emissions, whereas the need of emerging countries to maintain economic growth and development entails a sharp increase in energy consumption. However, to meet this, current energy systems need to be transformed. Several studies find different conclusions on the short-run and long-run relationship and the direction of causality, and none of the studies have considered energy efficiency in their model. This study investigates the direction of causality between energy efficiency, energy consumption, and economic growth in South Africa. To determine if a long-run relationship between the variables exists, the Johanson cointegration test is used, and the results indicate that there is a long-run relationship between economic growth, energy depletion, energy efficiency, non-renewable energy consumption, renewable energy consumption, and energy security, with trace statistics suggesting that the null hypothesis of no cointegration should be rejected at a 5% level of significance. The Toda and Yamamoto procedure of the Granger causality approach was then applied. This study finds a unidirectional causality between energy efficiency, non-renewable energy consumption, and economic growth and no causality between renewable energy consumption, energy depletion, energy security, and economic growth. The growth hypothesis is supported, while the neutrality hypothesis is only confirmed regarding renewable energy consumption and economic growth. The results further suggest that a unidirectional Granger causality exists between non-renewable consumption and energy efficiency, and economic growth in South Africa. In South Africa, energy efficiency is a significant tool to enhance sustainable growth and attain climate objectives. Also, energy efficiency helps to lower the costs of mitigating carbon emissions and further advance both social and economic development.

The Southern African Customs Union (SACU), as a bloc, is compelled to commit to trade in environmentally friendly goods. This study investigated the short-run and long-run relationships between trade openness and environmental quality in the SACU. The Cross-Sectional Autoregressive Distributed Lag (CS-ARDL) approach was applied to the data from 1985 to 2023. The results show that the estimated coefficients of trade openness positively and significantly contribute to carbon emissions in the short run and the long run. The results demonstrate that the gains-from-trade hypothesis does not hold in the SACU. Also, the results indicate that foreign direct investment inflow does not significantly contribute to CO₂ emissions; therefore, the pollution haven hypothesis does not hold. The Dumitrescu–Hurlin Granger non-causality test was employed, and the results show that there is bidirectional causality between CO₂ emissions and trade openness, CO₂ emissions and economic growth, and CO₂ emissions and population growth and no directional causality between foreign direct investment and CO₂ emissions. This study recommends that SACU countries should encourage the trade of eco-friendly goods, which is likely to lessen environmental consequences.