Applications of dispersive sum rules: ε-expansion and holography

Dean Carmi, Joao Penedones, Joao A. Silva, Alexander Zhiboedov

Research output: Contribution to journalArticlepeer-review


We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in d = 4 − ε dimensions. We re-derive many of the known results to order ε4 and we make new predictions. No assumption of analyticity down to spin 0 was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

Original languageEnglish
Article number145
JournalSciPost Physics
Issue number6
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© D. Carmi et al.

ASJC Scopus subject areas

  • General Physics and Astronomy


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