Conformal ghosts on the sphere

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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 \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.Comment: 11 + 2 pages, no figures, shortened, to be published in jm

On a Logarithmic Deformation of the Supersymmetric bc-system on Curved Manifolds

E. Frenkel, A. Losev and N. Nekrasov claim that a certain class of theories on compact Kahler manifolds and in particular the "gauged" supersymmetric bc-system on CP^1 are logarithmic conformal field theories. We discuss that proposition on a classical level for the bc-system on CP^1. The outcome of our investigation conforms to their conjecture. The property of being a logarithmic CFT thus can be interpreted as an effect of gravity