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 EguchiOoguri's version of Ward's equations and certain types of BPZ equations on a torus.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 DOI:
 10.48550/arXiv.1708.07361
 arXiv:
 arXiv:1708.07361
 Bibcode:
 2017arXiv170807361K
 Keywords:

 Mathematical Physics;
 Mathematics  Complex Variables;
 Mathematics  Probability
 EPrint:
 86 pages