相关论文: Theta functions on Noncommutative T^4
We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra $A_{\theta}$. The exact solutions of these provide various generalisations of the Powers-Rieffel projection. By identifying the…
We define the theta group associated to a simple coherent sheaf $\cal F$ on a hyperk\"ahler manifold $X$ of Kummer type or OG6 type, provided $g^{*}({\cal F})$ is isomorphic to $\cal F$ for every automorphism $g$ of $X$ acting trivially on…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
In this paper, we construct gauge bundles on a noncommutative toroidal orbifold $T^4_\theta/Z_2$. First, we explicitly construct a bundle with constant curvature connections on a noncommutative $T^4_\theta$ following Rieffel's method. Then,…
In this paper we give a proof of the Gauss-Bonnet theorem of Connes and Tretkoff for noncommutative two tori $\mathbb{T}_{\theta}^2$ equipped with an arbitrary translation invariant complex structure. More precisely, we show that for any…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
In the context of noncommutative space-time, we investigate the nucleon structure functions which plays an important role to identify the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in…
In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…
We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A. Polishchuk. Our aim is to understand how these rings give rise to an arithmetic structure on the noncommutative torus. We start by giving…
We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In…
In this article, we explicitly construct a canonical basis for the space of certain weakly holomorphic Drinfeld modular forms for $\Gamma_0(T)$ (resp., for $\Gamma_0^+(T)$) and compute the generating function satisfied by the basis…
Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
We compute the $\theta$-dependent mass spectrum of the 2-flavor Schwingr model using the tensor network (DMRG) in the Hamiltonian formalism. The pion and the sigma meson are identified as stable particles of the model for nonzero $\theta$…
We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them…
We describe an algorithm for computing the inner product between a holomorphic modular form and a unary theta function, in order to determine whether the form is orthogonal to unary theta functions without needing a basis of the entire…
We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
Let $\theta$ be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for $\langle |\theta|^2, \varphi \rangle$ as $\varphi$ traverses a…
This is a report on a joint work [12] with D. Essouabri, C. Levy and A. Sitarz. The spectral action on noncommutative torus is obtained, using a Chamseddine--Connes formula via computations of zeta functions. The importance of a Diophantine…
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative…