Some aspects of conformal field theories on the plane and higher genus Riemann surfaces

Pramana ◽  
1990 ◽  
Vol 35 (3) ◽  
pp. 205-286 ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Riemann Surfaces ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

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.

Higher genus partition functions of meromorphic conformal field theories

2009 ◽  
Vol 2009 (06) ◽  
pp. 048-048 ◽  
Author(s):  
Matthias R Gaberdiel ◽  
Roberto Volpato
Keyword(s):  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

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.

CORRELATORS OF CONFORMAL FIELD THEORIES FROM THEIR CHARACTERS

1990 ◽  
Vol 05 (31) ◽  
pp. 2643-2649
Author(s):  
R. P. MALIK ◽  
N. BEHERA ◽  
R. K. KAUL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complete Solution ◽  
Arbitrary Point ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

All genus characters define a complete solution of a two-dimensional rational conformal field theory. An arbitrary point correlator can be obtained by an appropriate combination of the pinchings of zero-homology and non-zero-homology cycles of the characters on the higher genus Riemann surface.

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