GLOBAL CHIRAL VERTEX OPERATORS ON RIEMANN SURFACES

1992 ◽  
Vol 04 (03) ◽  
pp. 425-449 ◽  
Author(s):  
L. BONORA ◽  
F. TOPPAN
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Riemann Surfaces ◽  
Vertex Operators ◽  
Affine Algebras ◽  
Higher Genus ◽  
Level 1

Using Krichever-Novikov bosonic oscillators we introduce chiral vertex operators on a higher genus Riemann surface Σ. These are essentially the normal-ordered exponential of line integrals of connections in a suitable line bundle over Σ. We discuss globally defined affine algebras in Σ and use chiral vertices to construct level 1 representations of the latter.

scholarly journals Padé approximants on Riemann surfaces and KP tau functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Marco Bertola
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Hilbert Problem ◽  
Line Bundles ◽  
Fixed Degree ◽  
Tau Function ◽  
Tau Functions ◽  
Deformation Parameters ◽  
Higher Genus ◽  
Geometric Solutions

AbstractThe paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resulting Padé-like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal sections, in a similar fashion to the ordinary orthogonal polynomial case. The second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing between two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev–Petviashvili hierarchy with respect to either deformation parameters, and a certain modification of the 2-Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro-geometric solutions.

BOSONIZATION AND FERMION VERTICES ON AN ARBITRARY GENUS RIEMANN SURFACE BY USING A GLOBAL OPERATOR FORMALISM

1989 ◽  
Vol 04 (24) ◽  
pp. 2349-2362 ◽  
Author(s):  
JORGE RUSSO
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Explicit Computation ◽  
Operator Formalism ◽  
Central Extensions ◽  
Arbitrary Topology ◽  
Global Operator ◽  
Arbitrary Genus ◽  
Higher Genus ◽  
Spin Fields

Fermi-Bose equivalence is studied with the use of a global operator formalism on Riemann surfaces of arbitrary topology. The quantization of a scalar field on a circle is performed in detail, globally, at arbitrary genus. A new algebra of the Krichever-Novikov type naturally emerges. This admits three central extensions and generalizes standard algebras of the sphere to higher genus. It is shown by explicit computation that the central terms, as well as correlation functions, corresponding to the Bose and Fermi models agree. Spin fields and fermion vertices are defined within this framework and their conformal properties are investigated.

HIGHER GENUS WAVEFUNCTION OF ANYON SYSTEM

1991 ◽  
Vol 06 (02) ◽  
pp. 163-170
Author(s):  
JNANADEVA MAHARANA ◽  
SUDHAKAR PANDA
Keyword(s):  
Correlation Function ◽  
Riemann Surfaces ◽  
Scalar Fields ◽  
Vertex Operators ◽  
Arbitrary Genus ◽  
Higher Genus ◽  
Free Scalar

A method is proposed for constructing the wavefunction of anyons on Riemann surfaces of arbitrary genus. This has been carried out in the framework of computing the correlation function of the chiral vertex operators, involving free scalar fields, with appropriate external momenta. Our technique, as a check, reproduces the already known anyonic wavefunction on the sphere as well as that on the torus.

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

Level-one SU(3) Wess-Zumino model on higher-genus Riemann surfaces

1990 ◽  
Vol 41 (2) ◽  
pp. 478-483 ◽  
Author(s):  
R. K. Kaul ◽  
R. P. Malik ◽  
N. Behera
Keyword(s):  
Riemann Surfaces ◽  
Higher Genus ◽  
Zumino Model

Equivariant Forms: Structure and Geometry

2013 ◽  
Vol 56 (3) ◽  
pp. 520-533 ◽  
Author(s):  
Abdelkrim Elbasraoui ◽  
Abdellah Sebbar
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Modular Forms ◽  
Differential Forms ◽  
Cross Ratio ◽  
Canonical Line Bundle ◽  
The Cross

Abstract.In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of SL2(ℤ) by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

scholarly journals SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM

2001 ◽  
Vol 16 (05) ◽  
pp. 822-855 ◽  
Author(s):  
JUAN MALDACENA ◽  
CARLOS NUÑEZ
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Field Theories ◽  
De Sitter ◽  
Curved Manifolds ◽  
Conformal Field ◽  
Low Energies ◽  
M Theory

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form Rd×Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS5. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

scholarly journals Analytic Functions on Some Riemann Surfaces

1963 ◽  
Vol 22 ◽  
pp. 211-217 ◽  
Author(s):  
Nobushige Toda ◽  
Kikuji Matsumoto
Keyword(s):  
Riemann Surface ◽  
Compact Subset ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Open Riemann Surface ◽  
Interesting Theorem ◽  
Hyperbolic Riemann Surface

Some years ago, Kuramochi gave in his paper [5] a very interesting theorem, which can be stated as follows.THEOREM OF KURAMOCHI. Let R be a hyperbolic Riemann surface of the class Of OHR(OHD,resp.). Then, for any compact subset K of R such that R—K is connected, R—K as an open Riemann surface belongs to the class 0AB(OAD resp.).

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