Anomalous symmetries end at the boundary

Ryan Thorngren (Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, 02138, USA) ; Yifan Wang (Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, 02138, USA; efferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA)

A global symmetry of a quantum field theory is said to have an ’t Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in the presence of a boundary. We then recast the problem in terms of symmetry defects and find the same conclusions for anomalies of discrete and orientation-reversing global symmetries, up to the conjecture that global gravitational anomalies, which may not be associated with any diffeomorphism symmetry, also forbid the existence of boundary conditions. This conjecture holds for known gravitational anomalies in D ≤ 3 which allows us to conclude the obstruction result for D ≤ 4.

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      "source": "Springer", 
      "value": "A global symmetry of a quantum field theory is said to have an \u2019t Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in the presence of a boundary. We then recast the problem in terms of symmetry defects and find the same conclusions for anomalies of discrete and orientation-reversing global symmetries, up to the conjecture that global gravitational anomalies, which may not be associated with any diffeomorphism symmetry, also forbid the existence of boundary conditions. This conjecture holds for known gravitational anomalies in D \u2264 3 which allows us to conclude the obstruction result for D \u2264 4."
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Published on:
03 September 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 9
Pages 1-36
DOI:
https://doi.org/10.1007/JHEP09(2021)017
arXiv:
2012.15861
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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