Related papers: On Twisted Virasoro Operators and Number Theory
We calculate mean values of $\operatorname{GL}_n$-automorphic $L$-functions twisted by primitive even Dirichlet characters of prime-power conductor, at arbitrary points within the critical strip, by derivation of special Voronoi summation…
We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which is a semi-direct sum of Virasoro algebra and its module.…
Let $F$ be a non-archimedean local field of characteristic zero, let $(\pi,V)$ be an irreducible, admissible representation of $\GSp(4,F)$ with trivial central character, and let $\chi$ be a quadratic character of $F^\times$ with conductor…
It is known that the Takahashi--Tanimoto identity-based solution in open string field theory derives a kinetic operator which is a sum of twisted Virasoro generators. Applying the infinite circumstance description of conformal field theory,…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…
We construct symmetry generators and operators for $J\bar{T}$-deformed conformal field theories by generalizing the framework established for $T\bar{T}$ deformations. Working in the Hamiltonian formalism on the plane, we derive the symmetry…
Conformal field theory and its axiomatisation in terms of vertex operator algebras or chiral algebras are most commonly considered on the Riemann sphere. However, an important constraint in physics and an interesting source of mathematics…
Let $d$ be a real number, let $s$ be in a fixed compact set of the strip $1/2<\sigma<1$, and let $L(s, \chi)$ be the Dirichlet $L$-function. The hypothesis is that for any real number $d$ there exist 'many' real numbers $\tau$ such that the…
Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…
For a rational valued periodic function, we associate a Dirichlet series and provide a new necessary and sufficient condition for the vanishing of this Dirichlet series specialized at positive integers. This question was initiated by…
A vertex algebra with an action of a group $G$ comes with a notion of $g$-twisted modules, forming a $G$-crossed braided tensor category. For a Lie group $G$, one might instead wish for a notion of $(\mathrm{d}+A)$-twisted modules for any…
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…
Some identities between unitary minimal Virasoro characters at levels 3, 4 and 5 are shown to arise as a consequence of relations between Artin L-functions of different quadratic fields. The definitions and concepts of number theory…
Dirichlet's theorem guarantees infinitely many primes in each reduced residue class modulo q, but the analytic mechanism underlying this separation is often difficult to visualize directly. In this article we construct simplified…
The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…
Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…
The Le Roy function has been the focus of intensive research in recent years, owing both to its relevance in analysis and its versatility in applications involving fractional differential operators. Other special functions - such as the…
It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…