Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2021)017
Keywords
Anomalies in Field and String Theories; Discrete Symmetries; Global Symmetries; Space-Time Symmetries
Categories
Funding
- Center for Mathematical Sciences and Applications at Harvard University
- Center for the Fundamental Laws of Nature at Harvard University
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This paper discusses the impact of the 't Hooft anomaly symmetry, including the obstruction to defining symmetric boundary conditions and the results regarding gravitational anomalies. By analyzing the Wess-Zumino consistency conditions and current Ward identities, we demonstrate the obstruction to theories with perturbative anomalies.
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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