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

Chi-Ming Chang Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Ying-Hsuan Lin Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA; Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74020

SciPost Physics, 10, (119), 2021.5
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)×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).
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  title={On exotic consistent anomalies in (1+1)d: A ghost story},
  author={Chi-Ming Chang, and Ying-Hsuan Lin},
  booktitle={SciPost Physics},
Chi-Ming Chang, and Ying-Hsuan Lin. On exotic consistent anomalies in (1+1)d: A ghost story. 2021. Vol. 10. In SciPost Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702143836972101516.
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