Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 8, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP08(2014)152
Keywords
Anomalies in Field and String Theories; Renormalization Group
Categories
Funding
- Swiss National Science Foundation [200020-138131, 200020-150060]
- Swiss National Science Foundation (SNF) [200020_138131] Funding Source: Swiss National Science Foundation (SNF)
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The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the beta-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving the trace of the energy-momentum tensor. We use the latter result to give a fully detailed proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also correspond to CFTs. We also clarify the relation between the matrix entering the gradient flow formula for the beta-function and a manifestly positive metric in coupling space associated with matrix elements of the trace of the energy momentum tensor.
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