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

Chang, Chi-Ming and Lin, Ying-Hsuan (2020) On Exotic Consistent Anomalies in (1+1)d: A Ghost Story. . (Unpublished)

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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 potentially uplifting U(1) to a multifold cover. We end with a survey of the holomorphic bc ghost system, which realizes all the exotic consistent anomalies.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Chang, Chi-Ming0000-0002-8978-2613
Lin, Ying-Hsuan0000-0001-8904-1287
Additional Information: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.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
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Record Number:CaltechAUTHORS:20200930-100727133
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105667
Deposited By: Joy Painter
Deposited On:30 Sep 2020 17:16
Last Modified:30 Sep 2020 17:16

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