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arXiv · 1401.5983

The local Callan-Symanzik equation: structure and applications

Florent Baume·Boaz Keren-Zur·Riccardo Rattazzi·Lorenzo Vitale
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Abstract

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 $β$-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 $β$-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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Florent Baume, Boaz Keren-Zur, Riccardo Rattazzi, Lorenzo Vitale. 2015-10-29. The local Callan-Symanzik equation: structure and applications. https://doi.org/10.1007/jhep08(2014)152

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