scholarly journals Conformal field theories on Riemann surfaces of genus $g \geq 1$

2014 ◽  
Vol 0074 ◽  
pp. 25-25
Author(s):  
M. Leitner
Keyword(s):  
Riemann Surfaces ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

DIFFERENTIAL EQUATIONS IN g≥2 CONFORMAL FIELD THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 1773-1782
Author(s):  
AKISHI KATO ◽  
TOMOKI NAKANISHI
Keyword(s):  
Differential Equations ◽  
Riemann Surfaces ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Highest Weight ◽  
Higher Genus ◽  
Highest Weight Representations ◽  
Null State

We consider the minimal conformal field theories on Riemann surfaces of genus greater than one. We illustrate in a simple example how the null state conditions in the highest weight representations of the Virasoro algebra turn into differential equations including the moduli variables for correlators between degenerate fields. In particular, the set of an infinite number of partial differential equations satisfied by higher genus characters is obtained.

CONFORMAL FIELD THEORY ON Zk-SURFACES WITH EXCHANGE INTERACTIONS

1998 ◽  
Vol 13 (35) ◽  
pp. 2863-2871 ◽  
Author(s):  
VINCENZO MAROTTA ◽  
ANTONINO SCIARRINO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surfaces ◽  
Exchange Interactions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

We consider a class of conformal field theories on Riemann surfaces represented as a Zk invariant covering of the sphere. The introduction of exchange interactions among couples of sheets generate effective parafermions. The outgoing theory can be seen as a fractional supersymmetry conformal field theory.

scholarly journals C=1 conformal field theories on Riemann surfaces

1988 ◽  
Vol 115 (4) ◽  
pp. 649-690 ◽  
Author(s):  
Robbert Dijkgraaf ◽  
Erik Verlinde ◽  
Herman Verlinde
Keyword(s):  
Riemann Surfaces ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

NONSTANDARD CONFORMAL FIELD THEORIES FROM THE b-c SYSTEMS ON GENERAL ALGEBRAIC CURVES

1996 ◽  
Vol 11 (12) ◽  
pp. 2213-2229 ◽  
Author(s):  
F. FERRARI ◽  
J. SOBCZYK
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Algebraic Curves ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Operator Formalism ◽  
Normal Ordering ◽  
Conformal Field ◽  
Complex Sphere ◽  
Free Scalar

In this paper we develop an operator formalism for the b–c systems with conformalweight λ=1 defined on a general closed and orientable Riemann surface. The advantageof our approach is that the Riemann surface is represented as an affine algebraic curve.In this way it is possible to show that the b–c systems at higher genera are equivalentto nonstandard conformal field theories on the complex sphere. The amplitudes of theseconformal field theories, rigorously computed using simple normal ordering prescriptions,are single-valued on the algebraic curve and coincide with the correlation functions of theoriginal b–c systems. Besides the obvious applications in string theories and conformalfield theories, (the b–c systems at λ=1 are intimately related to the free scalar fieldtheory), the operator formalism presented here also sheds some light on the quantizationof field theories on Riemann surfaces.

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