The topology of moduli space and quantum field theory

David Montano*, Jacob Sonnenschein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show how an SO(2,1) gauge theory with a fermionic symmetry may be used to describe the topology of the moduli space of curves. The observables of the theory correspond to the generators of the cohomology of moduli space. This is an extension of the topological quantum field theory introduced by Witten to investigate the cohomology of Yang-Mills instanton moduli space. We explore the basic structure of topological quantum field theories, examine a toy U(1) model, and then realize a full theory of moduli space topology. We also discuss why a pure gravity theory, as attempted in previous work, could not succeed.

Original languageEnglish
Pages (from-to)348-370
Number of pages23
JournalNuclear Physics, Section B
Issue number2
StatePublished - 25 Sep 1989
Externally publishedYes


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