Related papers: Hyperbolic and trigonometric hypergeometric soluti…
We construct three-dimensional N=2 supersymmetric conformal field theories on conic spaces. Built upon the fact that the partition function depends solely on the Reeb vector of the Killing vector, we propose that holographic dual of these…
The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…
The Gauge/YBE correspondence states a surprising connection between solutions to the Yang-Baxter equation with spectral parameters and partition functions of supersymmetric quiver gauge theories. This correspondence has lead to systematic…
In this paper we determine solutions for the L\'evy-Leblond operator or a parabolic Dirac operator in terms of hypergeometric functions and spherical harmonics. We subsequently generalise our approach to a wider class of Dirac operators…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
The purpose of this article is to demonstrate that i) the framework of elliptic hypergeometric integrals (EHIs) can be extended by input from supersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIs in the extended…
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum/integrals associated to the $A_n$ and $BC_n$ root systems, generalising the formulas previously obtained by Rains. The sum/integrals are expressed in…
This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual…
A certain two-dimensional supersymmetric gauge theory is argued to satisfy a relation that promotes the Zamolodchikov tetrahedron equation to an infrared duality between two quantum field theories. Solutions of the tetrahedron equation with…
The n-dimensional hypergeometric integrals associated with a hypersphere arrangement are formulated by the pairing of n-dimensional twisted cohomology and its dual. Under the condition of general position there are stated some results which…
We introduce the Hyperbolic Higgs, a novel solution to the little hierarchy problem that features Standard Model neutral scalar top partners. At one-loop order, the protection from ultraviolet sensitivity is due to an accidental non-compact…
In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius)…
We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and…
The most recent studies on the supersymmetric localization reveal many non-trivial features of supersymmetric field theories in diverse dimensions, and 3d gauge theory provides a typical example. It was conjectured that the index and the…
We study the connection between $N=2$ supersymmetry and a topological bound in a two-Higgs-doublet system with an $SU(2)\times U(1)_Y\times U(1)_{Y^{\prime}}$ gauge group. We derive the Bogomol'nyi equations from supersymmetry…
We show that nontrivial solutions to higher and fractional order equations with certain nonlinearity are radially symmetric and nonincreasing on geodesic balls in the hyperbolic space $\mathbb{H}^n$ as well as on the entire space…
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational…
We produce a decomposition of the parameter space of the $A$-hypergeometric system associated to a projective monomial curve as a union of an arrangement of lines and its complement, in such a way that the analytic behavior of the solutions…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…