Kavli Affiliate: Tom Melia
| First 5 Authors: Tom Melia, Sridip Pal, , ,
| Summary:
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.
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