Large-N limit of the gradient flow in the 2D O (N) nonlinear sigma model

The gradient flow equation in the 2D O(N) nonlinear sigma model with lattice regularization is solved in the leading order of the 1/N expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy-momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-N method. This analysis confirms that the above lattice energy-momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap.