A Field-theoretical Interpretation of the Holographic Renormalization Group
Abstract
A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of finite local counterterms is discussed in detail, as well as its implications for the holographic C function. We also discuss issues special to the situation when mass deformations are present. Furthermore we suggest that the holographic RG equation may also be obtained from a bulk diffeomorphism which reduces to a Weyl transformation on the boundary.
Cite
@article{arxiv.hep-th/0103219,
title = {A Field-theoretical Interpretation of the Holographic Renormalization Group},
author = {Johanna Erdmenger},
journal= {arXiv preprint arXiv:hep-th/0103219},
year = {2009}
}
Comments
24 pages, LaTeX, no figures; references added, typos corrected, paragraph added to section 6