Bosonization on higher genus Riemann surfaces

@article{AlvarezGaum1987BosonizationOH,
  title={Bosonization on higher genus Riemann surfaces},
  author={Lu{\'i}s Alvarez-Gaum{\'e} and Jean-Beno{\^i}t Bost and Gregory W. Moore and Philip C. Nelson and Cumrun Vafa},
  journal={Communications in Mathematical Physics},
  year={1987},
  volume={112},
  pages={503-552}
}
We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global considerations require that we add new topological terms to the bosonic action. The proof that our prescription is correct relies on methods of complex algebraic geometry. 
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