Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

Hiroki Makino, Hiroshi Suzuki

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Original languageEnglish
Article number033B08
JournalProgress of Theoretical and Experimental Physics
Issue number3
Publication statusPublished - Nov 7 2014

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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