Long-range multi-scalar models at three loops - Archive ouverte HAL
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2020

Long-range multi-scalar models at three loops

Dario Benedetti
Razvan Gurau
Sabine Harribey
Kenta Suzuki

Résumé

Abstract We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power 0 < ζ < 1, rendering the computation of Feynman diagrams much harder than in the usual short-range case ( ζ = 1). As a consequence, previous results stopped at two loops, while seven-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an ϵ = 4 ζ − d expansion at fixed dimension d < 4, extensively using the Mellin–Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: O ( N ), ( Z 2 ) N ⋊ S N , and O ( N ) × O ( M ). For such models, we compute the fixed points and critical exponents.

Dates et versions

hal-04457045 , version 1 (14-02-2024)

Identifiants

Citer

Dario Benedetti, Razvan Gurau, Sabine Harribey, Kenta Suzuki. Long-range multi-scalar models at three loops. Journal of Physics A: Mathematical and Theoretical, 2020, 53 (44), pp.445008. ⟨10.1088/1751-8121/abb6ae⟩. ⟨hal-04457045⟩

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