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

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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 nonperturbative mass gap.