Pure gauge SU(2) Seiberg-Witten theory and modular forms

We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with the Weierstrass curve C ∕ L ∍ z ↦ ( 1 , ℘ ( z ) , ℘ ( z ) ′ ) and thereby obtain explicitely a modular form from which the moduli space parameter u and lattice parameters a and a D can be derived in terms of modular, respe...

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Bibliographic Details
Published in:Journal of mathematical physics 2007-08, Vol.48 (8), p.083505-083505-10
Main Authors: Vogeler, Kirsten, Flohr, Michael
Format: Article
Language:English
Subjects:
CONFORMAL INVARIANCE
Correlation analysis
Exact sciences and technology
FUNCTIONS
GAUGE INVARIANCE
LATTICE FIELD THEORY
LATTICE PARAMETERS
Mathematical functions
Mathematical methods in physics
Mathematics
Parameter identification
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Sciences and techniques of general use
SU-2 GROUPS
Theory
TRIPLETS
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Summary:We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with the Weierstrass curve C ∕ L ∍ z ↦ ( 1 , ℘ ( z ) , ℘ ( z ) ′ ) and thereby obtain explicitely a modular form from which the moduli space parameter u and lattice parameters a and a D can be derived in terms of modular, respectively, theta functions. We further discuss its relationship with the c = − 2 triplet model conformal field theory.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2759443