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arXiv · 1412.8218

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

Hiroki Makino·Fumihiko Sugino·Hiroshi Suzuki
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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.

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Hiroki Makino, Fumihiko Sugino, Hiroshi Suzuki. 2014-12-28. Large-$N$ limit of the gradient flow in the 2D $O(N)$ nonlinear sigma model. https://doi.org/10.1093/ptep%2Fptv044

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