scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

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.

scholarly journals Five-dimensional gauge theories on spheres with negative couplings

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Joseph A. Minahan ◽  
Anton Nedelin
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Simons Theory ◽  
Partition Functions ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Instanton Contribution ◽  
Sphere Radius ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We consider supersymmetric gauge theories on S5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)+N/2× SU(N/2)−N/2× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling of the SU(N/2)±N/2 is positive and infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)N/2 pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and Nf< 8 fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

scholarly journals ADE SINGULARITY AND PREPOTENTIALS IN N=2 SUPERSYMMETRIC YANG–MILLS THEORY

1998 ◽  
Vol 13 (31) ◽  
pp. 5373-5390 ◽  
Author(s):  
KATSUSHI ITO ◽  
SUNG-KIL YANG
Keyword(s):  
Toda Lattice ◽  
Complete Agreement ◽  
Gauge Groups ◽  
Yang Mills ◽  
Spectral Curves ◽  
Instanton Contribution ◽  
The One

We calculate the instanton corrections in the effective prepotential for N=2 supersymmetric Yang–Mills theory with all ADE gauge groups from the Seiberg–Witten geometry constructed out of the spectral curves of the periodic Toda lattice. The one-instanton contribution is determined explicitly by solving the Gauss–Manin system associated with the ADE singularity. Our results are in complete agreement with the ones obtained from the microscopic instanton calculations.

scholarly journals 𝒩 = 2 dualities and Z-extremization in three dimensions

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Brian Willett ◽  
Itamar Yaakov
Keyword(s):  
Three Dimensions ◽  
Partition Functions ◽  
Recent Proposal ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Seiberg Duality ◽  
Real Mass ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We use localization techniques to study duality in 𝒩 = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

Recommendations of The Ombudsman’s Dilemma: Between Law Enforcement Officials and Protection of Credibility

2018 ◽  
Vol 2 ◽  
pp. 1-12
Author(s):  
Dyah Adriantini Sintha Dewi
Keyword(s):  
Law Enforcement ◽  
Public Service ◽  
Public Services ◽  
Point Of View ◽  
Law Enforcement Officials ◽  
Muslim Majority ◽  
The Republic ◽  
The Government ◽  
The One ◽  
Oversight Body

The Ombudsman as an external oversight body for official performance, in Fikih Siyasah (constitutionality in Islam) is included in the supervision stipulated in legislation (al-musahabah al-qomariyah). Supervision is done so that public service delivery to the community is in accordance with the rights of the community. This is done because in carrying out its duties, officials are very likely to conduct mal administration, which is bad public services that cause harm to the community. The Ombudsman is an institution authorized to resolve the mal administration issue, in which one of its products is by issuing a recommendation. Although Law No. 37 of 2018 on the Ombudsman of the Republic of Indonesia states that the recommendation is mandatory, theombudsman's recommendations have not been implemented. This is due to differences in point of view, ie on the one hand in the context of law enforcement, but on the other hand the implementation of the recommendation is considered as a means of opening the disgrace of officials. Recommendations are the last alternative of Ombudsman's efforts to resolve the mal administration case, given that a win-win solution is the goal, then mediation becomes the main effort. This is in accordance with the condition of the Muslim majority of Indonesian nation and prioritizes deliberation in resolving dispute. Therefore, it is necessary to educate the community and officials related to the implementation of the Ombudsman's recommendations in order to provide good public services for the community, which is the obligation of the government.

Defending the Difference

2017 ◽  
Keyword(s):  
Social Sciences ◽  
Natural Sciences ◽  
Point Of View ◽  
True Nature ◽  
Natural Entities ◽  
The Social ◽  
The World ◽  
Methodological Difference ◽  
The Difference ◽  
The One

Dreyfus argues that there is a basic methodological difference between the natural sciences and the social sciences, a difference that derives from the different goals and practices of each. He goes on to argue that being a realist about natural entities is compatible with pluralism or, as he calls it, “plural realism.” If intelligibility is always grounded in our practices, Dreyfus points out, then there is no point of view from which one can ask about or provide an answer to the one true nature of ultimate reality. But that is consistent with believing that the natural sciences can still reveal the way the world is independent of our theories and practices.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Linkages between Energy Delivery and Economic Growth from the Point of View of Sustainable Development and Seaports

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4255
Author(s):  
Elżbieta Szaruga ◽  
Zuzanna Kłos-Adamkiewicz ◽  
Agnieszka Gozdek ◽  
Elżbieta Załoga
Keyword(s):  
Sustainable Development ◽  
Crude Oil ◽  
Cross Correlation ◽  
Point Of View ◽  
Oil Products ◽  
Modern Approach ◽  
Economic Cycles ◽  
Study Results ◽  
The One ◽  
Oil And Oil Products

This paper presents the synchronisation of economic cycles of GDP and crude oil and oil products cargo volumes in major Polish seaports. On the one hand, this issue fits into the concept of sustainable development including decoupling; on the other hand, the synchronisation may be an early warning tool. Crude oil and oil products cargo volumes are a specific barometer that predicts the next economic cycle, especially as they are primary sources of energy production. The research study applies a number of TRAMO/SEATS methods, the Hodrick–Prescott filter, spectral analysis, correlation and cross-correlation function. Noteworthy is the modern approach of using synchronisation of economic cycles as a tool, which was described in the paper. According to the study results, the cyclical components of the cargo traffic and GDP were affected by the leakage of other short-term cycles. However, based on the cross-correlation, it was proved that changes in crude oil and oil products cargo volumes preceded changes in GDP by 1–3 quarters, which may be valuable information for decision-makers and economic development planners.

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