Calculus of conformal fields on a compact Riemann surface

Abstract

We present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which represent the Lie derivative operators in terms of the Virasoro fields and the puncture operators associated with the background charges. As applications, we derive Eguchi-Ooguri's version of Ward's equations and certain types of BPZ equations on a torus.

86 pages

References in corpus (2)

• Highly Excited Strings I: Generating Function
• Radial SLE martingale-observables

Cited by in corpus (5)

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• Conformal field theory on the Riemann sphere and its boundary version for SLE