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Published May 28, 2021 | Published + Submitted
Journal Article Open

On exotic consistent anomalies in (1+1)d: A ghost story

Abstract

We revisit 't Hooft anomalies in (1+1)dd 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)dd 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)×SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)dd 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 bcbc 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).

Additional Information

© 2021 C. Chang and Y. Lin. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 16-12-2020; Accepted 16-04-2021; Published 28-05-2021. We are grateful to Po-Shen Hsin, Chao-Ming Jian, Shu-Heng Shao, Ryan Thorngren, Yifan Wang and Xiao-Gang Wen for helpful discussions and comments. CC thanks the hospitality of National Taiwan University. YL is supported by the Sherman Fairchild Foundation, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Collaboration Grant on the Non-Perturbative Bootstrap.

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Published - SciPostPhys_10_5_119.pdf

Submitted - 2009.07273.pdf

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