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EFT Asymptotics: the Growth of Operator Degeneracy

by Tom Melia, Sridip Pal

Submission summary

As Contributors: Sridip Pal
Arxiv Link: (pdf)
Date accepted: 2021-05-03
Date submitted: 2021-01-28 17:15
Submitted by: Pal, Sridip
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
  • Mathematical Physics
Approach: Theoretical


We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series -- partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.

Published as SciPost Phys. 10, 104 (2021)

Reports on this Submission

Anonymous Report 1 on 2021-2-15 (Contributed Report)


The authors addressed all pointsraised in my report, and I am ready to recommend the manuscript for SciPost publication.

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