Plasma beta effect on the $n=1$ Resonant Magnetic Perturbation (RMP) field penetration in purely radio-frequency (RF) wave heated discharges has been investigated in EAST. 
 Experimental results show that the dependence of threshold RMP coil current for field penetration, $I_{RMP,th}$, on the total absorbed power $P_{tot}$ scales as approximately $I_{RMP,th} \propto P_{tot}^{0.30}$, indicating that the error field tolerance is improved with increasing RF power. 
 This is benefited from the increased electron perpendicular flow dominated by counter current electron diamagnetic flow with increasing RF power. 
 However, theoretical scaling in cylindrical geometry overestimates the power index. 
 Assuming an additional term $\beta_N^{\alpha_{\beta_N}}$ for the normalized beta in the scaling, it is shown that the fitted $\alpha_{\beta_N}$ from the experimental observation is around $-1$, indicating an degradation effect of plasma beta.
 To clarify the underlying physics of plasma beta effect that was not included in the theoretical scaling in cylindrical geometry, the MARS-Q code with full toroidal geometry is employed for simulation of nonlinear field penetration (Liu \textit{et al} 2013 \textit{Phys. Plasmas} \textbf{20} 042503).
 The MARS-Q simulation results well reproduce the $\beta_N$ dependence and hence the $P_{tot}$ scaling of the threshold current in experimental observations.
 The main reason revealed that the net total torque, which is mainly contributed by the neoclassical toroidal viscosity (NTV), increases with increasing plasma $\beta_N$.
 The result demonstrates that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration even in this cases with relatively low $\beta_N \in [0.3,0.6]$, which is far less than no-wall beta limit.