Holographic renormalization for irrelevant operators and multi-trace counterterms

TL;DR

This paper explores holographic renormalization involving irrelevant operators, revealing new divergences and establishing a systematic renormalization approach with local and multi-trace counterterms.

Contribution

It introduces a systematic method to handle divergences from irrelevant operators using multi-trace counterterms in holographic renormalization.

Findings

Identified new non-local divergences in holographic renormalization.

Developed a renormalization scheme with local and multi-trace counterterms.

Clarified the relation between sources and bulk field asymptotics.

Abstract

We investigate the structure of holographic renormalization in the presence of sources for irrelevant operators. By working perturbatively in the sources we avoid issues related to the non-renormalizability of the dual field theory. We find new classes of divergences which appear to be non-local on the gravity side. However in all cases a systematic renormalization procedure exists involving either standard local counterterms or new counterterms which may be interpreted as multi-trace counterterms in the field theory. The multi-trace counterterms reflect a more intricate relation between sources and the asymptotics of bulk fields.