Abstract
Alvarez-Gaumé and Witten have shown that energy-momentum conservation must be violated in certain parity-violating quantum field theories involving gravity. In two dimensions this effect can be studied without the aid of Feynman diagrams or calculations in momentum space. The arguments parallel those for the conformal (trace) anomaly; as in that case, there are two kinds of arguments, one based on the conservation equations themselves with some very general assumptions, and the other based on explicit calculations and renormalization in a model theory with a linear field equation. The basic point is that if matter is created at all by the gravitational field, it must appear in both left-moving and right-moving modes if the conservation law is to hold always.
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This essay received an honourable mention (1985) by the Gravity Research Foundation—Ed.
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Fulling, S.A. The gravitational anomaly: An elementary, coordinate-space approach. Gen Relat Gravit 18, 609–615 (1986). https://doi.org/10.1007/BF00769929
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DOI: https://doi.org/10.1007/BF00769929