Correction exponents in the Gross–Neveu–Yukawa model at  $$1/N^2$$ 1 / N 2

Abstract

We calculate the critical exponents ω ± in the d-dimensional Gross-Neveu model in 1/N expansion with 1/N 2 accuracy. These exponents are related to the slopes of the β-functions at the critical point in the Gross-NeveuYukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations.

Easy-plane QED3’s in the large Nf limit

“…In 2+1d the large N f limit has recently been applied to calculate scaling dimensions of monopole operators, S 3 partition functions and central charges [52][53][54][55][56][57][58][59]. Other recent activity includes [60][61][62][63]. See also [64] for a review.…”

The β-function for Yukawa theory at large Nf

“…We leave the more detailed study within a general gauge-Yukawa framework for future work. Interestingly, the pure Yukawa model is closely related to the Gross-Neveu-Yukawa model, whose critical exponents have been recently computed up to 1/N 2 f [15,16]; see also the earlier studies on the Gross-Neveu model e.g. refs.…”

“…Here, we notice that the expression for Π (n) (p 2 , ), n ≥ 2, allows for the following expansion: 16) and π j (p 2 , ) are regular for → 0. Similarly to the previous cases, π 0 ( ) is independent of p 2 .…”

Bubble-resummation and critical-point methods for $$\beta $$-functions at large N

“…The explicit formulae for the O(1/N 2 ) coeffiecients can be found in Ref. [26] indicate that there is a new singularity not present at O(1/N ) occurring at t = 3. Correspondingly, this would suggest a shrinking in the radius of convergence for the β-functions when higher orders are included.…”

“…Nevertheless, the knowledge of ω ± can be used to obtain independent cross-checks and gain information regarding the radius of convergence of the 1/N expansion. The explicit formulae forω (1) ∓ are [25,26] ω (1)…”