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

### 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 Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

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

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.