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On Exotic Consistent Anomalies in (1+1)$d$: A Ghost Story

by Chi-Ming Chang, Ying-Hsuan Lin

Submission summary

As Contributors: Ying-Hsuan Lin
Preprint link: scipost_202102_00020v1
Date submitted: 2021-02-11 14:07
Submitted by: Lin, Ying-Hsuan
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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).

Current status:
Editor-in-charge assigned

Author comments upon resubmission

We thank the referee for comments, and have updated accordingly.

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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Resubmission scipost_202102_00020v1 on 11 February 2021

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