HIGHER GENUS WAVEFUNCTION OF ANYON SYSTEM

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.

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Weak Constraints in Conformal Field Theories on Higher-Genus Riemann Surfaces: Calculation of the Schwarzian Connection and Modified Vertex Operators

Progress of Theoretical Physics ◽

10.1143/ptp/87.3.743 ◽

1992 ◽

Vol 87 (3) ◽

pp. 743-755 ◽

Cited By ~ 1

Author(s):

G. Konisi ◽

T. Saito ◽

W. Takahasi

Keyword(s):

Riemann Surfaces ◽

Field Theories ◽

Vertex Operators ◽

Conformal Field Theories ◽

Conformal Field ◽

Higher Genus ◽

Weak Constraints

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

Modern Physics Letters A ◽

10.1142/s0217732389002641 ◽

1989 ◽

Vol 04 (24) ◽

pp. 2349-2362 ◽

Cited By ~ 1

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.

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GLOBAL CHIRAL VERTEX OPERATORS ON RIEMANN SURFACES

Reviews in Mathematical Physics ◽

10.1142/s0129055x9200011x ◽

1992 ◽

Vol 04 (03) ◽

pp. 425-449 ◽

Cited By ~ 3

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.

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q-HYPERGEOMETRIC FUNCTIONS IN THE FORMALISM OF FREE FIELDS

Modern Physics Letters A ◽

10.1142/s0217732393003275 ◽

1993 ◽

Vol 08 (30) ◽

pp. 2891-2902 ◽

Cited By ~ 14

Author(s):

ALEXEI MOROZOV ◽

LUC VINET

Keyword(s):

Hypergeometric Functions ◽

Riemann Sphere ◽

Scalar Fields ◽

Vertex Operators ◽

Free Scalar ◽

Free Fields

We describe a representation of the q-hypergeometric functions of one variable in terms of correlators of vertex operators made out of free scalar fields on the Riemann sphere.

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Padé approximants on Riemann surfaces and KP tau functions

Analysis and Mathematical Physics ◽

10.1007/s13324-021-00585-2 ◽

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.

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Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

Journal of High Energy Physics ◽

10.1007/jhep03(2021)045 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Yan Song ◽

Tong-Tong Hu ◽

Yong-Qiang Wang

Keyword(s):

Scalar Field ◽

Scalar Fields ◽

Cosmic Censorship ◽

Mass Ratio ◽

Quartic Coupling ◽

Scalar Theory ◽

Free Scalar ◽

The One ◽

Nonzero Scalar ◽

Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

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