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

Abstract

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.

arXiv comment16 pages, 6 figures, the final version to appear in PTEP

References in corpus (2)

• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Thermodynamics of SU(3) Gauge Theory from Gradient Flow

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• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
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