Exact Consequences of the Trace Anomaly in Four Dimensions

Details Exact Consequences of the Trace Anomaly in Four Dimensions Exact Consequences of the Trace Anomaly in Four Dimensions

2001-03-28

arxiv.org/abs/hep-th/0103237v2

Nucl.Phys. B618 (2001) 371-406

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 3 tables; published version, some misprints corrected; Mathematica routines can be found at: http://arturo.fi.infn

Scientific paper

10.1016/S0550-3213(01)00489-8

The general form of the stress-tensor three-point function in four dimensions is obtained by solving the Ward identities for the diffeomorphism and Weyl symmetries. Several properties of this correlator are discussed, such as the renormalization and scheme independence and the analogies with the anomalous chiral triangle. At the critical point, the coefficients a and c of the four-dimensional trace anomaly are related to two finite, scheme-independent amplitudes of the three-point function. Off-criticality, the imaginary parts of these amplitudes satisfy sum rules which express the total renormalization-group flow of a and c between pairs of critical points. Although these sum rules are similar to that satisfied by the two-dimensional central charge, the monotonicity of the flow, i.e. the four-dimensional analogue of the c-theorem, remains to be proven.

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