Related papers: Toric Amplitudes and Universal Adjoints
Let $X(\Delta)$ be the real toric variety associated to a smooth fan $\Delta$. The main purpose of this article is: (i) to determine the fundamental group and the universal cover of $X(\Delta)$, (ii) to give necessary and sufficient…
We studies the Newton polygon for the L-function of toric exponential sums attached to a family of two variable generalized hyperkloosterman sum,$f_{t}(x,y)=x^{n}+y+\frac{t}{xy}$ with $t$ the parameter. The explicit Newton polygon is…
In this paper, we provide a combinatorial description of seminormal toric varieties. The corresponding combinatorial object is a fan equipped with a collection of groups assigned to each cone. This framework introduces a more general class…
We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a…
The pion structure function is investigated in a simple model, where pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The imaginary part of the forward gamma* pi-> gamma* pi scattering amplitude is…
We predict an anomalous thermally activated superradiance in molecular aggregates within polaritonic environments. In contrast to free space, the collective emission is enhanced when either the exciton-phonon coupling or the temperature…
Let $X$ be a complete $\Q$-factorial toric variety of dimension $n$ and $\del$ the fan in a lattice $N$ associated to $X$. For each cone $\sigma$ of $\del$ there corresponds an orbit closure $V(\sigma)$ of the action of complex torus on…
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian…
We calculate the automorphism group of a complete toric variety $X$ with torus $T_M$. We prove that the radical unipotent of $Aut_k^0X$ is a semidirect product of additive groups, the reductive part is a quotient of a product of lineal…
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…
Carrollian amplitude is the natural object that defines the correlator of the boundary Carrollian field theory. In this work, we will elaborate on its proper definition in general dimensions. We use the vielbein field on the unit sphere to…
We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.
The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e. splits as a product…
We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…
An exact WKB treatment of 1-d homogeneous Schr\"odinger operators (with the confining potentials $q^N$, $N$ even) is extended to odd degrees $N$. The resulting formalism is first illustrated theoretically and numerically upon the spectrum…
Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce "stringy canonical forms", which provide a natural…
The method of self-adjoint extensions is employed to determine the vacuum quantum numbers induced by a singular static magnetic vortex in $2+1$-dimensional spinor electrodynamics. The results obtained are gauge-invariant and, for certain…
The global holomorphic \alpha-invariant introduced by Tian is closely related with the study in the existence of Kahler-Einstein metric. We apply the result of Tian, Lu and Zelditch on polarized Kahler metrics to approximate…
One-loop amplitudes may be expanded in a basis of scalar integrals multiplied by rational coefficients. We relate the coefficient of the one-point integral to the coefficients of higher-point integrals, by considering the effects of…