Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms

Details Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms

2006-07-20

arxiv.org/abs/hep-th/0607142v2

J.Math.Phys.48:083505,2007

Physics

High Energy Physics

High Energy Physics - Theory

11 + 2 pages, no figures, shortened, to be published in jmp

Scientific paper

10.1063/1.2759443

We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with the Weierstrass curve $\mathbbm{C}/L \ni z \mapsto (1,\wp(z),\wp(z)')$ and thereby obtain explicitely a modular form from which the moduli space parameter $u$ and lattice parameters $a$, $a_D$ can be derived in terms of modular respectively theta functions. We further discuss its relationship with the $c=-2$ triplet model conformal field theory.

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