Renormalisation of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow

Luigi del Debbio , Elizabeth Dobson , Andreas Jüttner , Ben Kitching-Morley , Joseph K.L. Lee , Valentin Nourry (1) , Antonin Portelli , Henrique Bergallo Rocha , Kostas Skenderis

1 APC (UMR_7164) - AstroParticule et Cosmologie

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of SU(N) with a φ4 interaction on the lattice. In this theory the energy-momentum tensor can mix with φ2 and we present numerical results for the mixing coefficient for the N=2 theory.

Mots clés: Lattice field theories; lattice QCD; tensor: energy-momentum; flow: Wilson; dimension: 3; tensor: energy-momentum: renormalization; field theory: scalar; lattice; SU(N); numerical calculations; strong coupling; nonperturbative; mixing

Domaines: Physique des Hautes Energies - Réseau [hep-lat]; Physique des Hautes Energies - Théorie [hep-th]

Luigi del Debbio, Elizabeth Dobson, Andreas Jüttner, Ben Kitching-Morley, Joseph K.L. Lee, et al.. Renormalisation of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow. Physical Review D, 2021, 103 (11), pp.114501. ⟨10.1103/PhysRevD.103.114501⟩. ⟨hal-02973155⟩