Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories

Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory, and borrowing ideas from compact geometry of the blowing up of affine ADE singularities, we build a class of local Calabi-Yau threefolds (CY^{3}) extending the local 2-torus model \mathcal{O}(m)\oplus \mathcal{O}(-m)\to T^{2\text{}} considered in hep-th/0406058 to test OSV conjecture. We first study toric realizations of T^{2} and then build a toric representation of X_{3} using intersections of local Calabi-Yau threefolds \mathcal{O}(m)\oplus \mathcal{O}(-m-2)\to \mathbb{P}^{1}. We develop the 2d \mathcal{N}=2 linear \sigma-model for this class of toric CY^{3}s. Then we use these local backgrounds to study partition function of 4d black holes in type IIA string theory and the underlying q-deformed 2d quiver gauge theories. We also make comments on 4d black holes obtained from D-branes wrapping cycles in \mathcal{O}(\mathbf{m}) \oplus \mathcal{O}(\mathbf{-m-2}%) \to \mathcal{B}_{k} with \mathbf{m=}(m_{1},...,m_{k}) a k-dim integer vector and \mathcal{B}_{k} a compact complex one dimension base consisting of the intersection of k 2-spheres S_{i}^{2} with generic intersection matrix I_{ij}. We give as well the explicit expression of the q-deformed path integral measure of the partition function of the 2d quiver gauge theory in terms of I_{ij}.Comment: 36 pages, latex, 9 figures. References adde

Review of blockchain-based distributed energy: Implications for institutional development

The future of energy is complex, with fluctuating renewable resources in increasingly distributed systems. It is suggested that blockchain technology is a timely innovation with potential to facilitate this future. Peer-to-peer (P2P) microgrids can support renewable energy as well as economically empower consumers and prosumers. However, the rapid development of blockchain and prospects for P2P energy networks is coupled with several grey areas in the institutional landscape. The purpose of this paper is to holistically explore potential challenges of blockchain-based P2P microgrids, and propose practical implications for institutional development as well as academia. An analytical framework for P2P microgrids is developed based on literature review as well as expert interviews. The framework incorporates 1) Technological, 2) Economic, 3) Social, 4) Environmental and 5) Institutional dimensions. Directions for future work in practical and academic contexts are identified. It is suggested that bridging the gap from technological to institutional readiness would require the incorporation of all dimensions as well as their inter-relatedness. Gradual institutional change leveraging community-building and regulatory sandbox approaches are proposed as potential pathways in incorporating this multi-dimensionality, reducing cross-sectoral silos, and facilitating interoperability between current and future systems. By offering insight through holistic conceptualization, this paper aims to contribute to expanding research in building the pillars of a more substantiated institutional arch for blockchain in the energy sector

Fano hypersurfaces and Calabi-Yau supermanifolds

In this paper, we study the geometrical interpretations associated with Sethi's proposed general correspondence between N = 2 Landau-Ginzburg orbifolds with integral \hat{c} and N = 2 nonlinear sigma models. We focus on the supervarieties associated with \hat{c} = 3 Gepner models. In the process, we test a conjecture regarding the superdimension of the singular locus of these supervarieties. The supervarieties are defined by a hypersurface \widetilde{W} = 0 in a weighted superprojective space and have vanishing super-first Chern class. Here, \widetilde{W} is the modified superpotential obtained by adding as necessary to the Gepner superpotential a boson mass term and/or fermion bilinears so that the superdimension of the supervariety is equal to \hat{c}. When Sethi's proposal calls for adding fermion bilinears, setting the bosonic part of \widetilde{W} (denoted by \widetilde{W}_{bos}) equal to zero defines a Fano hypersurface embedded in a weighted projective space. In this case, if the Newton polytope of \widetilde{W}_{bos} admits a nef partition, then the Landau-Ginzburg orbifold can be given a geometrical interpretation as a nonlinear sigma model on a complete intersection Calabi-Yau manifold. The complete intersection Calabi-Yau manifold should be equivalent to the Calabi-Yau supermanifold prescribed by Sethi's proposal.Comment: 24 pages, uses JHEP3.cls; v2: minor corrections, references adde

On F-theory Quiver Models and Kac-Moody Algebras

We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four dimensional base space. We focus on the base geometry which consists of intersecting F0=CP1xCP1 Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and indefinite, in particular hyperbolic. We interpret the equations defining these three classes of generalized Lie algebras as the anomaly cancelation condition of the corresponding N =1 F-theory quivers in four dimensions. We analyze in some detail hyperbolic geometries obtained from the affine A base geometry by adding a node, and we find that it can be used to incorporate fundamental fields to a product of SU-type gauge groups and fields.Comment: 13 pages; new equations added in section 3, one reference added and typos correcte