N=2 Generalized Superconformal Quiver Gauge Theory

Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.Comment: v2, reorganizing the materials, discussions on 2d CFT is remove

Superconformal indices of three-dimensional theories related by mirror symmetry

Recently, Kim and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by the mirror symmetry. The proofs are based on the well known identities of the theory of $q$-special functions. We also suggest the general index formula taking into account the $U(1)_J$ global symmetry present for abelian theories.Comment: 17 pages; minor change

Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

More Three Dimensional Mirror Pairs

We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One side of these mirror pairs are always the conventional quiver gauge theories. One of our result can also be used to determine the matter content and weakly coupled gauge groups of four dimensional N = 2 generalized quiver gauge theories derived from six dimensional A_N and D_N theory, therefore we explicitly constructed four dimensional S-duality pairs.Comment: 33 pages, 18 figures version2 minor correction

A bibliometric analysis of the 100 most-cited articles in dental materials journals

Background: Bibliometric studies are important as they provide an overview of research and scientific activity in a specific field. But studies of this type to determine the characteristics of the most cited articles in dental materials journals are completely lacking. Aim: To analyze the characteristics of 100 most-cited articles in dental materials journals since its inception through April 2019. Material and methods: Google scholar database was used to retrieve the list of journals titled with the term ‘‘dental materials”. A search was then conducted under "Publication Name" for each of the selected journals, and the articles were grouped by the category "Times Cited". The 100 highly cited papers published in five journals were contemplated in the eventual inquiry. The final collection was subjected to further scrutiny to determine the nature and characteristics of the documented revelations regard to journal name, year of publication, authors and their country, type of article, and area of research. Results: The 100 most-cited articles were published between 1985 and 2016 with maximum publications during 2001-05. The number of citations was ranging from 1926to 304. Only Dental Materials (97), Dental Materials Journal (3), shared the list.  The United States tops the list with 25 articles followed by Germany (12) and Belgium (11). Dental composites and adhesives were the most commonly addressed topics in dental materials journals. Conclusions: This bibliometric analysis connoted the evolving and interesting research trends in dental material science

Quivers, YBE and 3-manifolds

We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T^2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in H^3, each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph.The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results.Comment: 61 pages, 16 figures; v2: typos correcte