Critical exponent $\omega$ in the Gross-Neveu-Yukawa model at $O(1/N)$

The critical exponent $\omega$ is evaluated at $O(1/N)$ in $d$ dimensions in the Gross-Neveu model using the large $N$ critical point formalism. It is shown to be in agreement with the recently determined three-loop $\beta$-functions of the Gross-Neveu-Yukawa model in four dimensions. The same exponent is computed for the chiral Gross-Neveu and non-Abelian Nambu–Jona-Lasinio universality classes.

Figure 1

Leading order skeleton Schwinger-Dyson equations used to determine ${\omega }_1$ in the Gross-Neveu-Yukawa model.

Figure 2

Diagram corresponding to ${\mathrm{\Pi }}_{1B}$, where the double line indicates the inclusion of the correction to scaling exponent.

Figure 3

Feynman graph corresponding to ${\mathrm{\Pi }}_{1B}$ with exponents included, where $x$, $y$, and $z$ are the location of the vertices in coordinate space.

Figure 4

Feynman graph corresponding to ${\mathrm{\Pi }}_{1B}$ after conformal left transformation.

Figure 5

Leading order skeleton Schwinger-Dyson equations used to determine ${\omega }_1$ in the non-Abelian Nambu–Jona-Lasinio model.