scholarly journals Witten Genus and Elliptic Genera for Proper Actions

Author(s):  
Fei Han ◽  
Varghese Mathai
2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.


Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 630
Author(s):  
Hengtian Wang ◽  
Xiaolong Yang ◽  
Qihe Lou ◽  
Xinxin Xu

The Association of Southeast Asian Nations (ASEAN) has experienced rapid social and economic development in the past decades, while energy shortage, environmental pollution, and climate change are the factors that prevent a sustainable development process. Deployment of solar photovoltaic (PV) power is one of the effective alternatives to overcome the above barriers and assist ASEAN to achieve the aspirational target of 23% renewable energy (RE) in the total primary energy supply (TPES). In this study, SWOT analysis is adopted to analyze the internal strengths and weaknesses and the external threats and opportunities tightly related to the development of solar PV power in ASEAN countries. Through the SWOT analysis, great potential for the development of solar PV power in ASEAN is found. As long as appropriate policies are implemented and proper actions are taken, huge space for deployment of solar PV power can be expected. Based on the SWOT analysis, countermeasures that emphasize further deployment of solar PV power in ASEAN countries are put forward. The tactics include arousing people’s awareness of a sustainable development process, government issue coherence and stable incentive policies, fostering a solar PV industry chain and master key technology, and seek opportunities via an international cooperation.


2005 ◽  
Vol 16 (09) ◽  
pp. 941-955 ◽  
Author(s):  
ALI BAKLOUTI ◽  
FATMA KHLIF

Let G be a connected, simply connected nilpotent Lie group, H and K be connected subgroups of G. We show in this paper that the action of K on X = G/H is proper if and only if the triple (G,H,K) has the compact intersection property in both cases where G is at most three-step and where G is special, extending then earlier cases. The result is also proved for exponential homogeneous space on which acts a maximal subgroup.


2001 ◽  
Vol 146 (3) ◽  
pp. 595-687 ◽  
Author(s):  
M. Ando ◽  
M.J. Hopkins ◽  
N.P. Strickland
Keyword(s):  

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.


2021 ◽  
Author(s):  
Adel Mehrabadi ◽  
Gabriele Urbani ◽  
Simona Renna ◽  
Lucia Rossi ◽  
Italo Luciani ◽  
...  

Abstract In case of giant brown fields, a proper water injection management can result in a very complex process, due to the quality and quantity of data to be analysed. Main issue is the understanding of the injected water preferential paths, especially in carbonate environment characterized by strong vertical and areal heterogeneities (karst). A structured workflow is presented to analyze and integrate a massive data set, in order to understand and optimize the water injection scheme. An extensive Production Data Analysis (PDA) has been performed, based on the integration of available geological data (including NMR and Cased Hole Logs), production (allocated rates, Well Tests, PLT), pressure (SBHP, RFT, MDT, ESP) and salinity data. The applied workflow led to build a Fluid Path Conceptual Model (FPCM), an easy but powerful tool to visualize the complex dynamic connections between injectors-producers and aquifer influence areas. Several diagnostic plots were performed to support and validate the main outcomes. On this basis, proper actions were implemented to optimize the current water injection scheme. The workflow was applied on a carbonate giant brown field characterized by three different reservoir members, hydraulically communicating at original conditions, characterized by high vertical heterogeneity and permeability contrast. Moreover, dissolution phenomena, localized in the uppermost reservoir section, led to important permeability enhancement through a wide network of connected vugs, acting as water preferential communication pathways. The geological analysis played a key role to investigate the reservoir water flooding mechanism in dynamic conditions. The water rising mechanism was identified to be driven by the high permeability contrast, hence characterized by lateral independent movements in the different reservoir members. The integrated analysis identified room for optimization of the current water injection strategy. In particular, key factor was the analysis and optimization at block scale, intended as areal and vertical sub-units, as identified by the PDA and visualized through the FPCM. Actions were suggested, including injection rates optimization and the definition of new injections points. A detailed surveillance plan was finally implemented to monitor the effects of the proposed actions on the field performances, proving the robustness of the methodology. Eni workflow for water injection analysis and optimization was previously successfully tested only in sandstone reservoirs. This paper shows the robustness of the methodology also in carbonate environment, where water encroachment is strongly driven by karst network. The result is a clear understanding of the main dynamics in the reservoir, which allows to better tune any action aimed to optimize water injection and increase the value of mature assets.


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