TY - JOUR

T1 - The topology of moduli space and quantum field theory

AU - Montano, David

AU - Sonnenschein, Jacob

PY - 1989/9/25

Y1 - 1989/9/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0011608732&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(89)90470-7

DO - 10.1016/0550-3213(89)90470-7

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AN - SCOPUS:0011608732

SN - 0550-3213

VL - 324

SP - 348

EP - 370

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -