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On Exotic Consistent Anomalies in (1+1)$d$: A Ghost Story
by Chi-Ming Chang, Ying-Hsuan Lin
|As Contributors:||Ying-Hsuan Lin|
|Date submitted:||2021-02-11 14:07|
|Submitted by:||Lin, Ying-Hsuan|
|Submitted to:||SciPost Physics|
We revisit 't Hooft anomalies in (1+1)$d$ non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)$d$ classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1)$\times$SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)$d$ spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic $bc$ ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).
Author comments upon resubmission
List of changes
1- We rewrote the section "On the 'embedding' of anomalies of finite subgroups", and moved it later to improve the flow of the paper. The abstract and the introduction section are edited accordingly.
2- We added footnote 21 to mention a comment by the Referee.
Submission & Refereeing History
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