SciPost Submission Page
EFT Asymptotics: the Growth of Operator Degeneracy
by Tom Melia, Sridip Pal
- Published as SciPost Phys. 10, 104 (2021)
|As Contributors:||Sridip Pal|
|Arxiv Link:||https://arxiv.org/abs/2010.08560v2 (pdf)|
|Date submitted:||2021-01-28 17:15|
|Submitted by:||Pal, Sridip|
|Submitted to:||SciPost Physics|
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)
Submission & Refereeing History
You are currently on this page
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.