Generalized characters of the level-one Wess–Zumino–Witten model for simply laced groups on Riemann surfaces

1991 ◽  
Vol 69 (2) ◽  
pp. 146-153
Author(s):  
Jae Hoon Choi ◽  
Jae Kwan Kim
Keyword(s):  
Riemann Surfaces ◽  
Gaussian Model ◽  
Fusion Rules ◽  
Higher Genus ◽  
Homology Cycle

The generalized characters of the level-one Al, Dl, and El Wess–Zumino–Witten models on the higher genus Riemann surfaces are obtained from their behaviors under the pinching limit of the zero-homology cycles. It is important in the construction of the higher genus characters that these models have fusion rules of the same type as the rational Gaussian model. The two-point correlators are also obtained by pinching the nonzero-homology cycle.

LEVEL-ONE SU(N) WZNW MODELS ON HIGHER-GENUS RIEMANN SURFACES

1993 ◽  
Vol 08 (17) ◽  
pp. 2955-2972 ◽  
Author(s):  
M. ALIMOHAMMADI ◽  
H. ARFAEI
Keyword(s):  
Partition Function ◽  
Simple Form ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Modular Invariance ◽  
Fusion Rules ◽  
Group Manifold ◽  
Special Cases ◽  
Wznw Model ◽  
Higher Genus

Using factorization properties and fusion rules, we find the higher-genus partition function and two-point correlators for the SU (N)1 WZNW model. The result has simple form in terms of higher-genus theta functions on the group manifold. The previously known results of SU (2)1 and SU (3)1 are also obtained as special cases. This method, combined with other considerations such as modular invariance, can be extended to the nonsimply laced groups and higher-level WZNW models.

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.

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

SPURIONS IN FUNCTIONAL AND OPERATOR QUANTIZATION OF STRING THEORY AND HARMONIC GAUGE

1991 ◽  
Vol 06 (12) ◽  
pp. 1061-1068
Author(s):  
A.P. DEMICHEV ◽  
M.Z. IOFA
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Riemann Surfaces ◽  
Ward Identity ◽  
Brst Quantization ◽  
Higher Genus ◽  
The Difference ◽  
Lagrange Approach

We discuss the difference between the Lagrange and the operator BRST quantization in string theory on Riemann surfaces of higher genus. An example of the harmonic gauge yielding the non-anomalous BRST Ward identity in the path integral Lagrange approach is studied in detail.

scholarly journals Induced Polyakov supergravity on Riemann surfaces of higher genus

1994 ◽  
Vol 11 (4) ◽  
pp. 767-784 ◽  
Author(s):  
Jean-Pierre Ader ◽  
Hamid Kachkachi
Keyword(s):  
Riemann Surfaces ◽  
Higher Genus
Sign in / Sign up

Export Citation Format

Share Document