相关论文: Exceptional Indices
Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…
We provide a systematic method to deduce the global form of flavor symmetry groups in 4d N=2 theories obtained by compactifying 6d N=(2,0) superconformal field theories (SCFTs) on a Riemann surface carrying regular punctures and possibly…
We investigate the unflavoured Schur indices of class $\mathcal S$ theories of modest rank, and in the case of $\mathcal{N}=4$ super Yang-Mills theory with special unitary gauge group of somewhat more general rank, with an eye towards their…
We introduce the basic elements of the theory of parametrized $\infty$-categories and functors between them. These notions are defined as suitable fibrations of $\infty$-categories and functors between them. We give as many examples as we…
We propose a new modeling and estimation approach to select the optimal treatment regime from different options through constructing a robust estimating equation. The method is protected against misspecification of the propensity score…
We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a…
In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
We provide general formulae for the topologically twisted index of a general three-dimensional ${\cal N}\geq 2$ gauge theory with an M-theory or massive type IIA dual in the large $N$ limit. The index is defined as the supersymmetric path…
Superconformal indices (SCIs) of 4d ${\mathcal N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4, E_6, E_7, E_8$ gauge groups this yields first examples of integrals of such…
We propose a general strategy to build three-dimensional gauge theories with four supercharges which enjoy a supersymmetry enhancement in the IR. The resulting IR SCFTs admit topological twists with particularly nice properties, as well as…
Let $\mathbb C$ be the set of complex numbers, and let $\mathcal P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P\in\mathcal P$ depends on at least two variables, we classify all possibilities for…
We present a new gauging of maximal supergravity in five spacetime dimensions with gauge group containing ISO(5), involving the local scaling symmetry of the metric, and admitting a supersymmetric anti-de Sitter vacuum. We show this maximal…
The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In…
We study the superconformal index of 3d $\mathcal{N}=2$ superconformal field theories on $S^1\times_{\omega} S^2$ in the Cardy-like limit where the radius of the $S^1$ is much smaller than that of the $S^2$. We show that the first two…