Renormalization group procedure for potential $-g/r^2$

Abstract

Schrödinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of $g$.

6 pages, 3 figures

References in corpus (6)

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Cited by in corpus (5)

• Asymptotic safety of gravity, the Higgs boson mass and beyond the Standard Model physics
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• Homoclinic RG flows, or when relevant operators become irrelevant
• Holographic RG flows and boundary conditions in a 3D gauged supergravity
• Momentum approach to the $1/r^2$ potential as a toy model of the Wilsonian renormalization