Gradient flow coupling in the SU(2) gauge theory with two adjoint fermions

We study SU(2) gauge theory with two fermion flavors in the adjoint representation. Using a clover improved HEX smeared action and the gradient flow running coupling allows us to simulate with larger lattice size than before. We find an infrared fixed point after a continuum extrapolation in the range $4.3\lesssim g^{*2}\lesssim 4.8$. We also measure the mass anomalous dimension and find the value $0.25\lesssim {\gamma }^{*}\lesssim 0.28$ at the fixed point.

Figure 1

The measured values of the gradient flow coupling against $L/a$ at different values of $\beta =4/g_0^2$. The dashed line indicates the perturbative running coupling in continuum at $\beta =4$ at $L/a=24$.

Figure 2

Left: The continuum extrapolation of the step scaling function at a few values of $u=g^2$. Right: The scaled continuum step scaling function $\sigma (u,2)/u$. The dashed line with the light green area depicts the second order continuum fit using all lattice sizes and the associated statistical error. The red curve with the red hashed area depicts the second order extrapolation with $L/a=6$ excluded and the solid black curve with the light blue area gives the third order fit.

Figure 3

Power law fits to the step scaling function. From left to right: Constrained, $n_a=2$, $n=5$ and $n_f^2=5$; unconstrained, $n_a=2$, $n=5$ and $n_f^2=5$; constrained, $n=4$, $n_a=3$, $n_f^2=4$, and $n_f^3=2$; constrained with smallest lattice excluded, $n=4$, $n_a=2$, $n_f^2=4$, and $n_f^3=2$. The green band shows the statistical error of the continuum extrapolation.

Figure 4

Left: The continuum extrapolation of the estimator for the anomalous dimension $\overline{\gamma }(u)$ at a few values of $u$. Right: The continuum limit of $\overline{\gamma }(u)$.