2D CFT blocks for the 4D class Sk\mathcal{S}_k theories

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the $\mathcal{N} = 1$ gauge theories. We find that the blocks corresponding to the SU(N) $\mathcal{S}_k$ gauge theories involve fields in certain non-unitary representations of the $W_{kN}$ algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D $\mathcal{N} = 1$ SCFTs of class $\mathcal{S}_k$.Comment: 42 pages,5 figure

Instanton counting in Class Sk\mathcal{S}_k

We compute the instanton partition functions of $\mathcal{N}=1$ SCFTs in class $\mathcal{S}_k$. We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the worldvolume of $K$ D(p-4) branes. Starting with D5/D1 setups probing a $\mathbb{Z}_\ell\times \mathbb{Z}_k$ orbifold singularity we obtain the $K$ instanton partition functions of 6d $(1,0)$ theories on $\mathbb{R}^4 \times T^2$ in the presence of orbifold defects on $T^2$ via computing the 2d superconformal index of the worldvolume theory on $K$ D1 branes wrapping the $T^2$. We then reduce our results to the 5d and to the 4d instanton partition functions. For $k=1$ we check that we reproduce the known elliptic, trigonometric and rational Nekrasov partition functions. Finally, we show that the instanton partition functions of $SU(N)$ quivers in class $\mathcal{S}_k$ can be obtained from the class $\mathcal{S}$ mother theory partition functions with $SU(kN)$ gauge factors via imposing the `orbifold condition' $a_{\mathcal{A}} \rightarrow a_A e^{2\pi i j/k}$ with $\mathcal{A}=jA$ and $A=1,\dots, N$, $j=1,\dots, k$ on the Coulomb moduli and the mass parameters.Comment: 43 pages, 7 figure

Guidelines for the preparation of budgets in not-for-profit organizations

In the absence of clear and acceptable measures for outcomes, the budget is probably the most important managerial tool for nonprofits. Nevertheless many nonprofits operate without a budget at all, or with a limited version of a budget that is used solely for fundraising with no managerial role. The purpose of this paper is to present guidelines for the preparation of budgets that can serve all the aspects of the organization's activity. More specifically the budget should provide the organization's management with tools for decision making, risk management, measuring efficiency and the ability to present a cleat picture of the organization's activities to internal and external stakeholders. The adoption of these guidelines may benefit both nonprofits and their donors. Nonprofits will be able to improve the way they manage their programs while donors will be able to get a clearer picture of the organization and to simplify their procedures for grant applications.nonprofits; management; budget; guide

Exact Bremsstrahlung and Effective Couplings

We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the $\mathcal{N}=4$ SYM ones, we obtain interpolating functions $f(g^2)$ such that a given $\mathcal{N}=2$ SCFT observable is obtained by replacing in the corresponding $\mathcal{N}=4$ SYM result the coupling constant by $f(g^2)$. These "exact effective couplings" encode the finite, relative renormalization between the $\mathcal{N}=2$ and the $\mathcal{N}=4$ gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.Comment: 16 pages, 10 pages appendices, 4 figures. v2, journal versio

Toda 3-Point Functions From Topological Strings

We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In arXiv:1310.3841 we computed the partition function of 5D $T_N$ theories on $S^4 \times S^1$ and suggested that they should be interpreted as the three-point structure constants of q-deformed Toda. In this paper, we provide the exact AGT-W dictionary for this relation and rewrite the 5D $T_N$ partition function in a form that makes taking the 4D limit possible. Thus, we obtain a prescription for the computation of the partition function of the 4D $T_N$ theories on $S^4$, or equivalently the undeformed 3-point Toda structure constants. Our formula, has the correct symmetry properties, the zeros that it should and, for $N=2$, gives the known answer for Liouville CFT.Comment: 51 pages, 6 figure

The performance of the finnish labour markets in the 1990s

The paper deals with performance of local labour markets in Finland. The gross-stream labour statistics provide useful tool for this analysis. The subject of the research is the working-aged population. The local labour markets are divided into three classes: major cities, regional centres and smaller centres. The periods of observation are years 1990-91 and 1996-97 in the stream data. During the former period Finland was sliding into depression, whilst in the latter period it was rising out of that same depression. Competence and know-how are important elements in regional development. They are intimately connected with the creation of, and accessibility to the high quality workforce needed by each region, as well as the in the general interest of the region as a whole, in particular with regard to the prospective location of profitable economic activities. Regional development is linked to migration and population development. Higher education and other institutions have proved to be important in population development.

CoFeD: A visualisation framework for comparative quality evaluation

Evaluation for the purpose of selection can be a challenging task particularly when there is a plethora of choices available. Short-listing, comparisons and eventual choice(s) can be aided by visualisation techniques. In this paper we use Feature Analysis, Tabular and Tree Representations and Composite Features Diagrams (CFDs) for profiling user requirements and for top-down profiling and evaluation of items (methods, tools, techniques, processes and so on) under evaluation. The resulting framework CoFeD enables efficient visual comparison and initial short-listing. The second phase uses bottom-up quantitative evaluation which aids the elimination of the weakest items and hence the effective selection of the most appropriate item. The versatility of the framework is illustrated by a case study comparison and evaluation of two agile methodologies. The paper concludes with limitations and indications of further work