Related papers: Exceptional Indices

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$-modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are…

By filling in missing values in datasets, imputation allows these datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost…

Following a recent work of Dolan and Osborn, we consider superconformal indices of four dimensional ${\mathcal N}=1$ supersymmetric field theories related by an electric-magnetic duality with the SP(2N) gauge group and fixed rank flavour…

We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We focus on the case when the fiber is a once-punctured torus (\Sigma_{1,1}). The corresponding 3d field theories can be realized using duality…

We explain why the concept of a spontaneously broken superconformal symmetry is useful to describe inflationary models favored by the Planck. Non-minimal coupling of complex scalars to curvature, N(X, X*) R, is compulsory for superconformal…

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string…

We evaluate the superconformal index of the Y^{p,q} quiver gauge theories using Romeslberger's prescription. For the conifold quiver Y^{1,0} we find exact agreement at large N with a previous calculation in the dual AdS_5 X T^{1,1}…

We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of N=1 theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential…

Supersymmetric theories involving a spontaneously broken flavor symmetry can solve the flavor-changing problem while having quark and lepton masses derived from both $F$ and $D$ terms. As an example, a theory of leptons is constructed in…

The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…

By looking at decidable quotients, a sufficient condition is provided to guarantee that (1) the full subcategory of decidable objects of a topos is an exponential ideal and that (2) the classical notion of connectedness for an object $X$…

We consider D-term hybrid inflation in the framework of superconformal supergravity. In part of the parameter space, inflation continues for subcritical inflaton field value. Consequently, a new type of inflation emerges, which gives…

We propose and test a novel conjectural relation satisfied by the superconformal index of maximally supersymmetric $U(N)$ gauge theory in four dimensions. Analogous relations appear to be also valid for the superconformal indices of a large…

This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…

In arXiv:0811.1909 Spiridonov and Vartanov, using the superconformal index technique, found that 4-dimensional N=1 SQCD theory with SU(2) gauge group and four flavors has 72 dual representations. Recently in arXiv:1209.1404 the authors…

For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…

We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…

We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…