An Algebraic geometry study of the b-c system with arbitrary twist fields and arbitrary statistics

We present an analysis of the generalb−c system (including the β−γ system) on a compact Riemann surface of arbitrary genusg≧0 by postulating that its correlation functions should only have the singularities imposed by the operator product expansion (OPE) of the system. Studying a very (in fact optimally) general form of theb−c system, we prove rigorously that the standard practice of eliminating zero modes, and even the standard lagrangian, follow from the analyticity structure dictated by the OPE alone. We extend the analysis to consider the most general case of the presence of twist (e.g. spin) fields. We then determine all the possible correlation functions of theb−c system, with statistics unspecified, compatible with the OPE. On imposing Fermi and Bose statistics, we obtain the correlation functions of the fermionicb−c and β−γ systems, respectively.

field theory: conformal
dimension: 2
ghost
operator product expansion
correlation function
zero mode
spin: statistics
statistics: spin
Riemann surface
geometry: algebra

References(25)

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