Browsing by Subject "BETA-FUNCTION"

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  • Ryttov, Thomas A.; Tuominen, Kimmo (2019)
    We consider a non-Abelian gauge theory with N-f fermions and discuss the possible existence of a non-trivial UV fixed point at large N-f . Specifically, we study the anomalous dimension of the (rescaled) glueball operator Tr F-2 to first order in 1/N-f by relating it to the derivative of the beta function at the fixed point. At the fixed point the anomalous dimension violates its unitarity bound and so the (rescaled) glueball operator is either decoupled or the fixed point does not exist. We also study the anomalous dimensions of the two spin-1/2 baryon operators to first order in 1/N-f for an SU(3) gauge theory with fundamental fermions and find them to be relatively small and well within their associated unitarity bounds.
  • Leino, Viljami; Rindlisbacher, Tobias; Rummukainen, Kari; Sannino, Francesco; Tuominen, Kimmo (2020)
    We present the first numerical study of the ultraviolet dynamics of nonasymptotically free gauge-fermion theories at large number of matter fields. As test bed theories, we consider non-Abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these numbers of flavors, asymptotic freedom is lost, and the theories are governed by a Gaussian fixed point at low energies. In the ultraviolet, they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow method can be successfully implemented and applied to determine the renormalized running coupling when asymptotic freedom is lost. Additionally, we prove that our analysis is connected to the Gaussian fixed point as our results nicely match with the perturbative beta function. Intriguingly, we observe that it is hard to achieve large values of the renormalized coupling on the lattice. This might be an early sign of the existence of a physical cutoff and imply that a larger number of flavors is needed to achieve the safe fixed point. A more conservative interpretation of the results is that the current lattice action is unable to explore the deep ultraviolet region where safety might emerge. Our work constitutes an essential step toward determining the ultraviolet fate of nonasymptotically free gauge theories.