Eta-invariants and anomalies in U1-Chern-Simons theory - Mathematics > Symplectic GeometryReport as inadecuate




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Abstract: This paper studies U1-Chern-Simons theory and its relation to aconstruction of Chris Beasley and Edward Witten. The natural geometric setuphere is that of a three-manifold with a Seifert structure. Based on asuggestion of Edward Witten we are led to study the stationary phaseapproximation of the path integral for U1-Chern-Simons theory after one ofthe three components of the gauge field is decoupled. This gives an alternativeformulation of the partition function for U1-Chern-Simons theory that isconjecturally equivalent to the usual U1-Chern-Simons theory. The goal ofthis paper is to establish this conjectural equivalence rigorously throughappropriate regularization techniques. This approach leads to some rathersurprising results and opens the door to studying hypoelliptic operators andtheir associated eta invariants in a new light.



Author: Lisa Jeffrey, Brendan McLellan

Source: https://arxiv.org/







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