Related papers: The Endless Beta Integrals
Let N be a manifold (with boundary) of dimension at least 3, such that its interior admits a hyperbolic metric of finite volume. We discuss the possible limits arising from sequences of relative fundamental cycles approximating the…
A series of conjectures is obtained as further investigation of the integral transformation I(alpha) introduced in the previous paper. A Macdonald-type difference operator D is introduced. It is conjectured that D and I(alpha) are…
We consider the Lee-Wick (LW) finite electrodynamics, i.e., the U(1) gauge theory where a (gauge-invariant) dimension-6 operator containing higher-derivatives is added to the free Lagrangian of the U(1) sector. Three bounds on the LW heavy…
The planar Landau system which describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field perpendicular to the plane, is explored within pedagogical settings aimed at the beginning graduate level.…
The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a U(1) field theory; in such a scheme a compact gauge group is deformed through a \gamma-parameter that varies along a non-compact internal direction, transverse…
We establish a positive product formula for the solutions of the Sturm-Liouville equation $\ell(u) = \lambda u$, where $\ell$ belongs to a general class which includes singular and degenerate Sturm-Liouville operators. Our technique relies…
Let $\Gamma$ be a torsion-free hyperbolic group. We study $\Gamma$--limit groups which, unlike the fundamental case in which $\Gamma$ is free, may not be finitely presentable or geometrically tractable. We define model $\Gamma$--limit…
A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative $ (\nabla F)^2 + F^3$ gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d…
We give three necessary and sufficient conditions so that a parabolic holomorphic semigroup $(\phi_t)$ in the unit disc is of finite shift. One is in terms of the asymptotic behavior of speeds of convergence, the second one is related to…
Continuous O$(d,d)$ global symmetries emerge in Kaluza-Klein reductions of $D$-dimensional string supergravities to $D-d$ dimensions. We show that the non-geometric elements of this group effectively act in the $D$-dimensional parent theory…
Under natural assumptions on the observable, we prove a Central Limit Theorem, a Berry-Esseen Theorem, and a quantitative Local Limit Theorem for a broad class of partially hyperbolic endomorphisms of the two-dimensional torus. Our results…
An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix…
In this work, we investigate new solutions to the decoration transformation in terms of various special functions, including the hyperbolic gamma function, the basic hypergeometric function, and the Euler gamma function. These solutions to…
In this paper, we introduce the concept of completely linear degeneracy for quasilinear hyperbolic systems in several space variables, and then get an interesting property for multidimensional hyperbolic conservation laws. Some examples and…
We study zeta functions enumerating submodules invariant under a given endomorphism of a finitely generated module over the ring of ($S$-)integers of a number field. In particular, we compute explicit formulae involving Dedekind zeta…
The Kamp\'{e} de F\'{e}riet double series $F_{1:1;1}^{1:1;1}$ is studied through the solution to the associated first-order nonhomogeneous differential equation. It is shown that the integral of $t^{\beta+l}M(\cdot;\beta;\lambda…
We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the…
The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gauss…
The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we…
Using differential renormalization, we calculate the complete two-point function of the background gauge superfield in pure N=1 Supersymmetric Yang-Mills theory to two loops. Ultraviolet and (off-shell) infrared divergences are renormalized…