Well, it’s been a minute.

Although I rarely write about physics on here (or much of anything these days), this is still technically a “research blog”, so I thought I might share an update for those of you who still have me in your RSS feeds.

First, David Poland and I showed that 3d Gross–Neveu–Yukawa CFTs have exactly two relevant scalars operators for N ≥ 2. In plain English, this means that if you’re looking for a quantum critical point in a fermionic system with a scalar order parameter, you only need to tune two parameters to reach it—as long as you have at least two kinds of fermions. The N=1 case corresponds to the super-Ising model, which does have a third relevant scalar and therefore lives in a 3d phase diagram.

(Strictly speaking, N refers to the number of Majorana degrees of freedom. In 3d, a Dirac spinor factorizes into four Majorana spinors, so a system with N/4 Dirac fermions will have a global symmetry group of O(N) or O(N/2)² ⋊ Z₂, depending on what the Yukawa coupling looks like. For more details, see appendix C of the “The Gross–Neveu–Yukawa archipelago”.)

Second, I contributed to a new bootstrap study of stress tensors in the critical 3d Ising model! Highlights include tighter bounds on critical exponents, bounds on the scaling dimensions of parity-odd operators, and some preliminary evidence that the Ising model is extremal in the space of CFTs. It’s also “1.3833683(35)% fermionic”—see our discussion section for an attempt to interpret this number.