Abstract
We consider the two-point functions of conserved bulk currents and energy-momentum tensor in a boundary CFT defined on ℝ1,2. Starting from the consistent forms of boundary gauge and gravitational anomalies we derive their respective contributions to the correlation functions in the form of anomalous Ward identities. Using the recently developed momentum space formalism we find an anomalous solution to each of these identities depending on a single undetermined form-factor. We study the solution in two different kinematic limits corresponding to small and large momentum pn, perpendicular to the boundary. We find that the anomalous term interpolates between a non-local form resembling the standard anomaly-induced term in a two-dimensional CFT at small pn and Chern-Simons contact terms at large pn. Using this we derive some consistency conditions regarding the dependence of these anomalies on the boundary conditions and discuss possible cancellation mechanisms. These ideas are then demonstrated on the explicit example of free, massless three-dimensional fermion. In particular we manage to obtain the respective anomalies via a diagrammatic momentum space computation and expose the well-known relation between bulk parity anomaly and boundary gauge anomalies.
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ArXiv ePrint: 1901.10920
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Prochazka, V. Boundary gauge and gravitational anomalies from Ward identities. J. High Energ. Phys. 2019, 47 (2019). https://doi.org/10.1007/JHEP07(2019)047
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DOI: https://doi.org/10.1007/JHEP07(2019)047